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A077835
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Expansion of 1/(1-2*x-2*x^2-2*x^3).
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4
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1, 2, 6, 18, 52, 152, 444, 1296, 3784, 11048, 32256, 94176, 274960, 802784, 2343840, 6843168, 19979584, 58333184, 170311872, 497249280, 1451788672, 4238699648, 12375475200, 36131927040, 105492203776, 307999212032, 899246685696, 2625476203008, 7665444201472
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the number of ways two opposing basketball teams could score a combined total of n points (counting one point free throws, two point field goals, and three point field goals) considering the order of the scoring as important. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443), Feb 07 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,2,2)
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FORMULA
| a(n)=sum{k=0..n, T(n-k, k)2^(n-k)}, T(n, k) = trinomial coefficients (A027907). - Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
a(n)=sum{k=0..n, sum{i=0..floor((n-k)/2), C(n-k-i, i)C(k, n-k-i)}*2^k} - Paul Barry (pbarry(AT)wit.ie), Apr 26 2005
a(n)= 2*a(n-1)+2*a(n-2)+2*a(n-3) [From Geoffrey Critzer (critzer.geoffrey(AT)usd443), Feb 07 2009]
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MATHEMATICA
| LinearRecurrence[{2, 2, 2}, {1, 2, 6}, 100] (* From Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)
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CROSSREFS
| Cf. A071675.
Sequence in context: A156989 A077935 * A077984 A052979 A005507 A094864
Adjacent sequences: A077832 A077833 A077834 * A077836 A077837 A077838
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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