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A213688
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a(n) = Sum_{i=0..n} A000129(i)^3.
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2
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0, 1, 9, 134, 1862, 26251, 369251, 5196060, 73113372, 1028784997, 14476099149, 203694183170, 2866194639170, 40330419190351, 567492063162119, 7985219303802744, 112360562315573112, 1581033091723823881, 22246823846444284881, 313036566941955454910
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x*(1-4*x-x^2)/((1-x)*(1+2*x-x^2)*(1-14*x-x^2)). [Bruno Berselli, Jun 18 2012]
a(n) = ((3+sqrt(2))*(1+sqrt(2))^(3n+1)+(3-sqrt(2))*(1-sqrt(2))^(3n+1)-21*(-1)^n*((1+sqrt(2))^n+(1-sqrt(2))^n)+32)/224. [Bruno Berselli, Jun 18 2012]
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MATHEMATICA
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LinearRecurrence[{13, 18, -42, 11, 1}, {0, 1, 9, 134, 1862}, 20] (* Bruno Berselli, Jun 21 2012 *)
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PROG
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(Magma) A110272:=func<n | n le 3 select Ceiling(n^2/2)^3 else 12*Self(n)+30*Self(n-1)-12*Self(n-2)-Self(n-3)>; [&+[A110272(i): i in [0..n]]: n in [0..19]]; // Bruno Berselli, Jun 21 2012
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CROSSREFS
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Cf. A110272 (cubes of the Pell numbers).
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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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