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 A145920 List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332). 5
 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 (list; graph; refs; listen; history; text; internal format)
 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: A117985 A115707 A117793 * A153785 A090294 A162540 Adjacent sequences:  A145917 A145918 A145919 * A145921 A145922 A145923 KEYWORD easy,nonn AUTHOR Matthew Vandermast, Oct 28 2008 STATUS approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)