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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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7
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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
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OFFSET
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0,2
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COMMENTS
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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. - Geoffrey Critzer, Feb 07 2009
Number of permutations of length a(n+1) avoiding the partially ordered pattern (POP) {1>3, 4>2} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the third element, and the fourth element is larger than the second element. - Sergey Kitaev, Dec 08 2020
a(n) is the number of compositions of n into parts 1, 3, and 3, each part of two kinds. - Joerg Arndt, Jul 30 2023
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LINKS
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FORMULA
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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} 2^k * Sum_{i=0..floor((n-k)/2)} C(n-k-i, i)*C(k, n-k-i). - Paul Barry, Apr 26 2005
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MATHEMATICA
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m={{2/3, 1/3, 0, 0}, {2/3, 0, 1/3, 0}, {2/3, 0, 0, 1/3}, {0, 0, 0, 0}};
initialState={{1, 0, 0, 0}};
Table[(initialState.MatrixPower[m, n])[[1, 4]]*3^n, {n, 3, 31}] (* Robert P. P. McKone, Jul 29 2023 *)
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PROG
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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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