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A164039
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a(n+1) = 3*a(n) - n.
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5
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1, 2, 4, 9, 23, 64, 186, 551, 1645, 4926, 14768, 44293, 132867, 398588, 1195750, 3587235, 10761689, 32285050, 96855132, 290565377, 871696111, 2615088312, 7845264914, 23535794719, 70607384133, 211822152374, 635466457096
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0) = 1; a(n+1) = 3*a(n) - n.
a(n) = (3^n + 2*n + 3)/4.
a(n) = 5*a(n-1)-7*a(n-2)+3*a(n-3).
G.f.: (1-3*x+x^2)/((1-3*x)*(1-x)^2). (End)
E.g.f.: (1/4)*((2*x + 3)*exp(x) + exp(3*x)). - G. C. Greubel, Sep 08 2017
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MATHEMATICA
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Transpose[NestList[Flatten[{Rest[#], ListCorrelate[#, {3, -7, 5}]}]&, {1, 2, 4}, 30]][[1]] (* Harvey P. Dale, Mar 24 2011 *)
Table[(3^n + 2*n + 3)/4, {n, 0, 50}] (* G. C. Greubel, Sep 08 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1-3*x+x^2)/((1-3*x)*(1-x)^2)) \\ G. C. Greubel, Sep 08 2017
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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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