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A266733
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a(n) = 21*binomial(n+6,7).
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2
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0, 21, 168, 756, 2520, 6930, 16632, 36036, 72072, 135135, 240240, 408408, 668304, 1058148, 1627920, 2441880, 3581424, 5148297, 7268184, 10094700, 13813800, 18648630, 24864840, 32776380, 42751800, 55221075, 70682976, 89713008, 112971936, 141214920, 175301280
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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 hexominoes (6-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=6 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)*(5+n)*(6+n)/240.
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8) for n>7.
G.f.: 21*x / (1-x)^8.
(End)
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MATHEMATICA
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Table[21 Binomial[n+6, 7], {n, 0, 40}] (* Harvey P. Dale, Jan 13 2021 *)
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PROG
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(PARI) a(n) = (n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(6+n))/240 \\ Colin Barker, Jan 08 2016
(PARI) concat(0, Vec(21*x/(1-x)^8 + O(x^40))) \\ Colin Barker, Jan 08 2016
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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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