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A005718
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Quadrinomial coefficients: C(2+n,n) + C(3+n,n) + C(4+n,n).
(Formerly M2918)
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7
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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FORMULA
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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).
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MAPLE
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MATHEMATICA
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Table[Plus@@Table[Binomial[i + n, n], {i, 2, 4}], {n, 0, 43}] (* From Alonso del Arte, Jun 14 2011 *)
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PROG
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(Magma) [(((n+14)*n+71)*n+130)*n/24+3: n in [0..45]]; // Vincenzo Librandi, Jun 15 2011
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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