Decagonal number

Decagonal number

A decagonal number is a figurate number that represents a decagon. The n-th decagonal number is given by the formula

Dn = 4n2 − 3n.

The first few decagonal numbers are:

0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326 (sequence A001107 in OEIS)

The n-th decagonal number can also be calculated by adding the square of n to thrice the (n—1)-th pronic number or, to put it algebraically, as

Dn = n2 + 3(n2n).

Properties

  • Decagonal numbers consistently alternate parity.

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Centered decagonal number — A centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. The centered decagonal number for n is given by the formula …   Wikipedia

  • 1000 (number) — List of numbers Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k → Cardinal 1000 one thousand …   Wikipedia

  • 2000 (number) — 2000 (two thousand) is the natural number following 1999 and preceding 2001.See also: millennium, year 2000 AD, Y2K, 2000 (disambiguation).Two thousand is the highest number expressible using only two unmodified characters in roman numerals… …   Wikipedia

  • 3000 (number) — 3000 (three thousand) is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English (when and is required from 101 forward). In other fields In the novel The Brothers Karamazov by Fyodor… …   Wikipedia

  • 4000 (number) — 4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number. Selected numbers in the range 4001 4999 * 4005 triangular number * 4007 safe prime * 4010 magic constant of n times; n normal magic square and …   Wikipedia

  • 5000 (number) — 5000 (five thousand) is the natural number following 4999 and preceding 5001. Five thousand is the largest isogrammic number in the English language. Selected numbers in the range 5001 5999 * 5003 Sophie Germain prime * 5020 amicable number with… …   Wikipedia

  • 6000 (number) — 6000 (six thousand) is the natural number following 5999 and preceding 6001. Selected numbers in the range 6001 6999 * 6025 Rhythm guitarist of the Dead Kennedys from June 1978 to March 1979. Full name is Carlos Cadona. * 6028 centered heptagonal …   Wikipedia

  • 7000 (number) — 7000 (seven thousand) is the natural number following 6999 and preceding 7001. Selected numbers in the range 7001 7999 * 7021 triangular number * 7043 Sophie Germain prime * 7056 84^2 * 7057 cuban prime of the form x = y + 1 * 7073 Leyland number …   Wikipedia

  • 9000 (number) — 9000 (nine thousand) is the natural number following 8999 and preceding 9001. List of numbers Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k → …   Wikipedia

  • 8000 (number) — 8000 (eight thousand) is the natural number following 7999 and preceding 8001.8000 is the cube of 20, as well as the sum of four consecutive integers cubed, 113 + 123 + 133 + 143.The fourteen tallest mountains on Earth, which exceed 8000 meters… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”