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A036800
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a(n) = -6 + 2^(n+1)*(3 - 2*n + n^2).
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12
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0, 2, 18, 90, 346, 1146, 3450, 9722, 26106, 67578, 169978, 417786, 1007610, 2392058, 5603322, 12976122, 29753338, 67633146, 152567802, 341835770, 761266170, 1686110202, 3716153338, 8153726970, 17817403386, 38788923386
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OFFSET
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0,2
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COMMENTS
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This sequence is a part of a class of sequences of the type: a(n) = sum(i=0,n,(C^i)*(i^k)). This sequence has C=2, k=2. Sequence A036799 has C=2, k=1. Suppose C>=2, k>=1 are integers. What is the general closed form for a(n)? - Ctibor O. Zizka, Feb 07 2008
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REFERENCES
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M. Petkovsek et al., A=B, Peters, 1996, p. 97.
Jolley, Summation of Series, Dover (1961), p. 6.
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LINKS
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FORMULA
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G.f.: 2*x*(1+2*x) / ( (1-x)*(1-2*x)^3 ).
a(0)=0, a(1)=2, a(2)=18, a(3)=90, a(n)=7*a(n-1)-18*a(n-2)+ 20*a(n-3)- 8*a(n-4). - Harvey P. Dale, Jun 13 2015
E.g.f.: 2*(3 -2*x +4*x^2)*exp(2*x) -6*exp(x). - G. C. Greubel, Mar 31 2021
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MAPLE
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MATHEMATICA
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LinearRecurrence[{7, -18, 20, -8}, {0, 2, 18, 90}, 30] (* Harvey P. Dale, Jun 13 2015 *)
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PROG
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(Sage) [2^(n+1)*(3-2*n+n^2) -6 for n in (0..30)] # G. C. Greubel, Mar 31 2021
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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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