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

1,3

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

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.

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

Example

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

Crossrefs

Cf. A141919, of which this is a subsequence.

Sequence in context: A371561 A115707 A117793 * A356179 A356132 A153785

Adjacent sequences: A145917 A145918 A145919 * A145921 A145922 A145923

Keyword

easy,nonn

Author

Matthew Vandermast, Oct 28 2008

Status

approved