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 A005718 Quadrinomial coefficients: C(2+n,n) + C(3+n,n) + C(4+n,n). (Formerly M2918) 6
 3, 12, 31, 65, 120, 203, 322, 486, 705, 990, 1353, 1807, 2366, 3045, 3860, 4828, 5967, 7296, 8835, 10605, 12628, 14927, 17526, 20450, 23725, 27378, 31437, 35931, 40890, 46345, 52328, 58872, 66011, 73780, 82215, 91353, 101232, 111891, 123370, 135710, 148953, 163142, 178321, 194535 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If Y is an (n-3)-subset of an n-set X then, for n>=5, a(n-5) is the number of 4-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007 This equation represents the number of numbers with <=n digits such that the sum of the digits is between 1 and 4 inclusive and no digit is larger than 3. - David Consiglio, Jr., Oct 27 2008 Row 2 of the convolution array A213548. - Clark Kimberling, Jun 20 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 = 0..1000 R. K. Guy, Letter to N. J. A. Sloane, 1987 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. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = binomial(n, 2)*(n^2+7*n+18)/12, n >= 2. G.f.: (x^2)*(3-3*x+x^2)/(1-x)^5 (numerator polynomial is N4(4, x) from A063421). a(n) = A008287(n, 4), n >= 2 (fifth column of quadrinomial coefficients). a(n) = A062745(n, 4), n >= 2 (fifth column). a(n) = 3*C(n+2,2) + 3*C(n+2,3) + C(n+2,4) (see comment in A071675). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012 MAPLE A005718:=-(3-3*z+z**2)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation MATHEMATICA Table[n (n + 1)/2! + n (n + 1) (n + 2)/3! + n (n + 1) (n + 2) (n + 3)/4!, {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *) Table[Plus@@Table[Binomial[i + n, n], {i, 2, 4}], {n, 0, 43}] (* From Alonso del Arte, Jun 14 2011 *) PROG (PARI) a(n)=(((n+14)*n+71)*n+130)*n/24+3 \\ Charles R Greathouse IV, Jun 14 2011 (MAGMA) [(((n+14)*n+71)*n+130)*n/24+3: n in [0..45]]; // Vincenzo Librandi, Jun 15 2011 CROSSREFS Sequence in context: A009135 A131740 A037237 * A199231 A098500 A037236 Adjacent sequences:  A005715 A005716 A005717 * A005719 A005720 A005721 KEYWORD nonn,easy AUTHOR EXTENSIONS Better description from Zerinvary Lajos, Dec 02 2005 STATUS approved

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Last modified April 26 04:11 EDT 2019. Contains 322469 sequences. (Running on oeis4.)