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A266732
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a(n) = 10*binomial(n+4, 5).
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3
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0, 10, 60, 210, 560, 1260, 2520, 4620, 7920, 12870, 20020, 30030, 43680, 61880, 85680, 116280, 155040, 203490, 263340, 336490, 425040, 531300, 657800, 807300, 982800, 1187550, 1425060, 1699110, 2013760, 2373360, 2782560, 3246320, 3769920, 4358970, 5019420
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OFFSET
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0,2
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COMMENTS
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Total number of pips on a set of tetrominoes (4-celled linear dominoes) with up to n pips in each cell.
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LINKS
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S. Butler, P. Karasik, A note on nested sums, J. Int. Seq. 13 (2010), 10.4.4, p=4 in the last equation on page 3.
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FORMULA
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a(n) = n*(1+n)*(2+n)*(3+n)*(4+n)/12.
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) for n > 5.
G.f.: 10*x / (1-x)^6.
(End)
E.g.f.: x*(120 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x)/12. - G. C. Greubel, Nov 24 2017
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MATHEMATICA
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Join[{0}, 10*Binomial[Range[0, 40]+5, 5]] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 10, 60, 210, 560, 1260}, 40] (* Harvey P. Dale, Jun 10 2016 *)
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PROG
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(PARI) a(n) = (n*(1+n)*(2+n)*(3+n)*(4+n))/12 \\ Colin Barker, Jan 08 2016
(PARI) concat(0, Vec(10*x/(1-x)^6 + O(x^50))) \\ Colin Barker, Jan 08 2016
(Magma) [10*Binomial(n+4, 5): n in [0..30]]; // G. C. Greubel, Nov 24 2017
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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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STATUS
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approved
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