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A321123
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a(n) = 2^n + 2*n^2 + 2*n + 1.
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2
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2, 7, 17, 33, 57, 93, 149, 241, 401, 693, 1245, 2313, 4409, 8557, 16805, 33249, 66081, 131685, 262829, 525049, 1049417, 2098077, 4195317, 8389713, 16778417, 33555733, 67110269, 134219241, 268437081, 536872653, 1073743685, 2147485633, 4294969409, 8589936837
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OFFSET
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0,1
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COMMENTS
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For n >= 2, a(n) is the number of evaluation points on the n-dimensional cube in Genz and Malik's degree 7 cubature rule.
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4), n >= 4.
G.f.: (2 - 3*x - 3*x^3)/((1 - 2*x)*(1 - x)^3).
E.g.f.: exp(2*x) + (1 + 4*x + 2*x^2)*exp(x).
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MATHEMATICA
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Table[2^n + 2*n^2 + 2*n + 1, {n, 0, 50}]
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PROG
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(Maxima) makelist(2^n + 2*n^2 + 2*n + 1, n, 0, 50);
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CROSSREFS
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Cf. A000051, A000079, A001787, A001844, A002064, A005126, A058331, A100314, A131830, A100314, A132750, A176691, A322593.
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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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