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 A000574 Coefficient of x^5 in expansion of (1 + x + x^2)^n. (Formerly M3011 N1219) 12
 3, 16, 51, 126, 266, 504, 882, 1452, 2277, 3432, 5005, 7098, 9828, 13328, 17748, 23256, 30039, 38304, 48279, 60214, 74382, 91080, 110630, 133380, 159705, 190008, 224721, 264306, 309256, 360096, 417384, 481712, 553707, 634032, 723387, 822510 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS If Y is a 3-subset of an n-set X then, for n>=7, a(n-4) is the number of 5-subsets of X having at most one element in common with Y. - Milan Janjic, Nov 23 2007 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). 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 = 3..1000 L. Carlitz et al., Permutations and sequences with repetitions by number of increases, J. Combin. Theory, 1 (1966), 350-374. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Eric Weisstein's World of Mathematics, Trinomial Coefficient Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA G.f.: x^3*(3-2*x)/(1-x)^6. a(n) = 3*binomial(n+2,5) - 2*binomial(n+1,5). a(n) = A111808(n,5) for n>4. - Reinhard Zumkeller, Aug 17 2005 a(n) = binomial(n+1, 4)*(n+12)/5 = 3*b(n-3)-2*b(n-4), with b(n)=binomial(n+5, 5); cf. A000389. a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Vincenzo Librandi, Jun 10 2012 a(n) = 3*binomial(n, 3) + 4*binomial(n, 4) + binomial(n, 5). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012 a(n) = GegenbauerC(N, -n, -1/2) where N = 5 if 5 GegenbauerC(`if`(5

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Last modified November 15 03:29 EST 2018. Contains 317224 sequences. (Running on oeis4.)