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A261724
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a(n) is the number of ways of putting n labeled balls into 4 indistinguishable boxes such that each box contains at least 3 balls.
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5
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15400, 200200, 1611610, 10335325, 57962905, 297797500, 1439774336, 6662393738, 29844199346, 130445781284, 559533979466, 2365296391535, 9885290914059, 40944327590760, 168389163468240, 688631376550260, 2803570746766140, 11373212443859760, 46006062639998890
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OFFSET
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12,1
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COMMENTS
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Linear recurrence signature is given by the terms of A255002 after -1. - Bruno Berselli, May 20 2016
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LINKS
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Colin Barker, Table of n, a(n) for n = 12..1000
I. Mezo, Periodicity of the last digits of some combinatorial sequences, arXiv preprint arXiv:1308.1637 [math.CO], 2013 (third formula on page 16 is incorrect).
Index entries for linear recurrences with constant coefficients, signature (30, -415, 3514, -20386, 85924, -272198, 661180, -1244717, 1822478, -2068955, 1802474, -1181760, 563888, -184752, 37152, -3456).
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FORMULA
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a(n) = (1/12)*(-3^(n - 2)*(n^2 + 5*n + 18) + (1/64)*(2^(2*n + 5) + 3*2^n*(n^4 + 2*n^3 + 19*n^2 + 42*n + 64) - 16*(n^6 - 9*n^5 + 43*n^4 - 91*n^3 + 112*n^2 - 32*n + 8))).
G.f.: x^12*(15400 -261800*x +1996610*x^2 -9045575*x^3 +27162905*x^4 -57079715*x^5 +86268721*x^6 -94696602*x^7 +75062256*x^8 -41952000*x^9 +15705360*x^10 -3538080*x^11 +362880*x^12) / ((1 -x)^7*(1 -2*x)^5*(1 -3*x)^3*(1 -4*x)). - Colin Barker, May 24 2016
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MATHEMATICA
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Table[(1/12) (-(3^(n - 2) (n^2 + 5 n + 18)) + (1/64) (2^(2 n + 5) + 3 2^n (n^4 + 2 n^3 + 19 n^2 + 42 n + 64) - 16 (n^6 - 9 n^5 + 43 n^4 - 91 n^3 + 112 n^2 - 32 n + 8))), {n, 12, 40}]
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PROG
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(MAGMA) [(1/12)*(-3^(n-2)*(n^2+5*n+18)+(1/64)*(2^(2*n+5)+3*2^n*(n^4+2*n^3+19*n^2+42*n+64)-16*(n^6-9*n^5+43*n^4-91*n^3+112*n^2-32*n+8))): n in [12..40]];
(PARI) Vec(x^12*(15400 -261800*x +1996610*x^2 -9045575*x^3 +27162905*x^4 -57079715*x^5 +86268721*x^6 -94696602*x^7 +75062256*x^8 -41952000*x^9 +15705360*x^10 -3538080*x^11 +362880*x^12) / ((1 -x)^7*(1 -2*x)^5*(1 -3*x)^3*(1 -4*x)) + O(x^30)) \\ Colin Barker, May 24 2016
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CROSSREFS
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Cf. A000478, A058844, A272352, A272982, column 4 of A059022.
Sequence in context: A345817 A252990 A252842 * A031637 A054838 A255148
Adjacent sequences: A261721 A261722 A261723 * A261725 A261726 A261727
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, May 17 2016
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EXTENSIONS
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Definition, data and formula corrected by Istvan Mezo and Bruno Berselli, May 20 2016
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STATUS
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approved
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