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A036827
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a(n) = 26 + 2^(n+1)*(-13 +9*n -3*n^2 +n^3).
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10
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0, 2, 34, 250, 1274, 5274, 19098, 63002, 194074, 567322, 1591322, 4317210, 11395098, 29392922, 74350618, 184942618, 453378074, 1097334810, 2626158618, 6222250010, 14610858010, 34032582682, 78693531674, 180757725210, 412685959194
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OFFSET
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0,2
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REFERENCES
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M. Petkovsek et al., A=B, Peters, 1996, p. 97.
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LINKS
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FORMULA
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G.f.: 2*x*(1 +8*x +4*x^2)/((1-x)*(1-2*x)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
a(n) = 9*a(n-1) -32*a(n-2) +56*a(n-3) -48*a(n-4) +16*a(n-5) for n>4 with a(0)=0, a(1)=2, a(2)=34, a(3)=250, a(4)=1274. - Harvey P. Dale, Dec 15 2011
E.g.f.: 2 (13*exp(x) + (-13 +14*x +8*x^3)*exp(2*x)). - G. C. Greubel, Mar 31 2021
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EXAMPLE
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a(3) = 2^0*0^3 + 2^1*1^3 + 2^2*2^3 + 2^3*3^3 = 250.
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MAPLE
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MATHEMATICA
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Table[26 +2^(n+1)(-13 +9n -3n^2 +n^3), {n, 0, 30}] (* or *) LinearRecurrence[ {9, -32, 56, -48, 16}, {0, 2, 34, 250, 1274}, 31] (* Harvey P. Dale, Dec 15 2011 *)
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PROG
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(Haskell)
a036827 n = 2^(n+1) * (n^3 - 3*n^2 + 9*n - 13) + 26
(Magma) [2*(13 + 2^n*(-13 +9*n -3*n^2 +n^3)): n in [0..35]]; // G. C. Greubel, Mar 31 2021
(Sage) [2*(13 + 2^n*(-13 +9*n -3*n^2 +n^3)) for n in (0..35)] # G. C. Greubel, Mar 31 2021
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CROSSREFS
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Cf. A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A232599 (p=3,q=-1), A126646 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), this sequence (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).
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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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