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A321124
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a(n) = (4*n^3 - 6*n^2 + 14*n + 3)/3.
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3
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1, 5, 13, 33, 73, 141, 245, 393, 593, 853, 1181, 1585, 2073, 2653, 3333, 4121, 5025, 6053, 7213, 8513, 9961, 11565, 13333, 15273, 17393, 19701, 22205, 24913, 27833, 30973, 34341, 37945, 41793, 45893, 50253, 54881, 59785, 64973, 70453, 76233, 82321, 88725
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OFFSET
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0,2
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COMMENTS
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For n >= 5, a(n) is the number of evaluation points on the n-dimensional cube in Phillips-Dobrodeev's degree 7 cubature rule.
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LINKS
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FORMULA
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a(n) = 8*binomial(n, 3) + 4*binomial(n, 2) + 4*binomial(n, 1) + 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n >= 4.
a(n) = a(n-1) + A128445(n+1), n >= 1.
E.g.f.: (1/3)*(3 + 12*x + 6*x^2 + 4*x^3)*exp(x).
G.f.: (1 + x - x^2 + 7*x^3)/(1 - x)^4.
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MATHEMATICA
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Table[(4*n^3 - 6*n^2 + 14*n + 3)/3, {n, 0, 50}]
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PROG
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(Maxima) makelist((4*n^3 - 6*n^2 + 14*n + 3)/3, n, 0, 50);
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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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