A145920 List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332).

0, 1, 5, 35, 70, 210, 330, 715, 1001, 1820, 2380, 3876, 4845, 7315, 8855, 12650, 14950, 20475, 23751, 31465, 35960, 46376, 52360, 66045, 73815, 91390, 101270, 123410, 135751, 163185, 178365, 211876, 230300, 270725, 292825, 341055, 367290, 424270

Offset: 1

Author

Matthew Vandermast, Oct 28 2008

Keywords

• easy
• nonn

Comments

All binomial coefficients C(n,4) belong to the generalized pentagonal sequence (A001318).

Pentagonal numbers of generalized pentagonal number (A001318) index number. - Raphie Frank, Nov 25 2012

Examples

			35, for example, is both A000326(5) and A000332(7).
		

Links

• William A. Tedeschi, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentagonal Number.
• Eric Weisstein's World of Mathematics, Pentatope Number.

Crossrefs

Cf. A141919, of which this is a subsequence.

Formula

a(n+1) = A000326 (A001318(n)).

Positive values of A000332(n) belong to the sequence if and only if 3 does not divide n. A000332(n) is positive when n>3.

Conjecture: a(n) = a(n-1) + 4a(n-2) - 4a(n-3) - 6a(n-4) + 6a(n-5) + 4a(n-6) - 4a(n-7) - a(n-8) + a(n-9). - R. J. Mathar, Oct 29 2008

Conjecture: G.f.: x^2(1 + 4x + 26x^2 + 19x^3 + 4x^5 + x^6 + 26x^4)/((1+x)^4(1-x)^5). - R. J. Mathar, Oct 29 2008

a(n) = (27x^4 - 18x^3 - 3x^2 + 2x)/8 where x = floor(n/2)*(-1)^n, for n >= 1. - William A. Tedeschi, Aug 16 2010