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 A053494 Number of symmetric 5 X 5 matrices of nonnegative integers with every row and column adding to n. 5
 1, 26, 348, 2698, 14751, 62781, 222190, 681460, 1865715, 4655535, 10756921, 23290026, 47700173, 93104473, 174248451, 314246511, 548380980, 929209095, 1533389605, 2470568045, 3894914166, 6019752376, 9136114923, 13635769173, 20039850376, 29033765566 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986; see Prop. 4.6.21, p. 235, G_5(lambda). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission] R. P. Stanley, Magic labelings of graphs, symmetric magic squares,..., Duke Math. J. 43 (3) (1976) 511-531, F_5(x) in Section 5. Index entries for linear recurrences with constant coefficients, signature (5,-4,-20,40,16,-100,44,110,-110,-44,100,-16,-40,20,4,-5,1). FORMULA G.f.: (1 + 21*x + 222*x^2 + 1082*x^3 + 3133*x^4 + 5722*x^5 + 7013*x^6 + 5722*x^7 + 3133*x^8 + 1082*x^9 + 222*x^10 + 21*x^11 + x^12) / ((1-x)^11*(1+x)^6). a(n) = (189*(59981+5555*(-1)^n) + 18*(2345165+65331*(-1)^n)*n + (76615494+689850*(-1)^n)*n^2 + 40*(2138179+6237*(-1)^n)*n^3 + (63277966+47250*(-1)^n)*n^4 + 1260*(25421+3*(-1)^n)*n^5 + 11171664*n^6 + 2644080*n^7 + 405954*n^8 + 36500*n^9 + 1460*n^10) / 12386304. - Colin Barker, Jan 14 2017 MATHEMATICA CoefficientList[Series[(1+21x+222x^2+1082x^3+3133x^4+5722x^5+7013x^6+5722x^7+3133x^8+1082x^9+222x^10+21x^11+x^12)/((1-x)^11(1+x)^6), {x, 0, 30}], x] (* or *) LinearRecurrence[ {5, -4, -20, 40, 16, -100, 44, 110, -110, -44, 100, -16, -40, 20, 4, -5, 1}, {1, 26, 348, 2698, 14751, 62781, 222190, 681460, 1865715, 4655535, 10756921, 23290026, 47700173, 93104473, 174248451, 314246511, 548380980}, 30] (* Harvey P. Dale, Mar 05 2023 *) PROG (PARI) Vec((1 + 21*x + 222*x^2 + 1082*x^3 + 3133*x^4 + 5722*x^5 + 7013*x^6 + 5722*x^7 + 3133*x^8 + 1082*x^9 + 222*x^10 + 21*x^11 + x^12) / ((1 - x)^11*(1 + x)^6) + O(x^30)) \\ Colin Barker, Jan 14 2017 CROSSREFS Cf. A019298, A053493. Sequence in context: A252826 A042306 A329300 * A054938 A161526 A161933 Adjacent sequences: A053491 A053492 A053493 * A053495 A053496 A053497 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 15 2000; revised definition, Jul 06 2014. STATUS approved

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Last modified September 28 04:27 EDT 2023. Contains 365721 sequences. (Running on oeis4.)