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 A005712 Coefficient of x^4 in expansion of (1+x+x^2)^n. (Formerly M4129) 28
 1, 6, 19, 45, 90, 161, 266, 414, 615, 880, 1221, 1651, 2184, 2835, 3620, 4556, 5661, 6954, 8455, 10185, 12166, 14421, 16974, 19850, 23075, 26676, 30681, 35119, 40020, 45415, 51336, 57816, 64889, 72590, 80955, 90021, 99826, 110409, 121810, 134070 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(n) = A111808(n,4) for n>3. - Reinhard Zumkeller, Aug 17 2005 If a 2-set Y and 2-set Z, having one element in common, are subsets of an n-set X then a(n-3) is the number of 5-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 03 2007 Antidiagonal sums of the convolution array A213781.  [Clark Kimberling, Jun 22 2012] REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..1000 Armen G. Bagdasaryan, Ovidiu Bagdasar, On some results concerning generalized arithmetic triangles, Electronic Notes in Discrete Mathematics (2018) Vol. 67, 71-77. R. K. Guy, Letter to N. J. A. Sloane, 1987 Milan Janjic, Two Enumerative Functions Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Eric Weisstein's World of Mathematics, Trinomial Coefficient Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (x^2)*(1+x-x^2)/(1-x)^5. a(n) = binomial(n+2,n-2) + binomial(n+1,n-2) - binomial(n,n-2). - Zerinvary Lajos, May 16 2006 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). Vincenzo Librandi, Jun 16 2012 a(n) = binomial(n,2) + 3*binomial(n,3) + binomial(n,4) (see our comment in A026729). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012 a(n) = GegenbauerC(N, -n, -1/2) where N = 4 if 4 GegenbauerC(`if`(4= 2 (fifth column of trinomial coefficients). Sequence in context: A272707 A266938 A299265 * A299278 A298741 A070893 Adjacent sequences:  A005709 A005710 A005711 * A005713 A005714 A005715 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Oct 02 2000 STATUS approved

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Last modified July 1 10:54 EDT 2022. Contains 354971 sequences. (Running on oeis4.)