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A077835 Expansion of 1/(1-2*x-2*x^2-2*x^3). 7
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; text; internal format)
OFFSET

0,2

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, Feb 07 2009]

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..2149

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.

Index entries for linear recurrences with constant coefficients, signature (2,2,2)

FORMULA

a(n) = sum{k=0..n, T(n-k, k)2^(n-k)}, T(n, k) = trinomial coefficients (A027907). - Paul Barry, 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, Apr 26 2005

a(n) = 2*a(n-1)+2*a(n-2)+2*a(n-3). [Geoffrey Critzer, Feb 07 2009]

MATHEMATICA

LinearRecurrence[{2, 2, 2}, {1, 2, 6}, 100] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

PROG

(PARI) Vec(1/(1-2*x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012

CROSSREFS

Cf. A071675.

Sequence in context: A078484 A156989 A077935 * A077984 A052979 A005507

Adjacent sequences:  A077832 A077833 A077834 * A077836 A077837 A077838

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)