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0, 1, 9, 45, 173, 573, 1725, 4861, 13053, 33789, 84989, 208893, 503805, 1196029, 2801661, 6488061, 14876669, 33816573, 76283901, 170917885, 380633085, 843055101, 1858076669, 4076863485, 8908701693, 19394461693, 42077257725, 90999619581, 196226318333
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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G.f.: x*(1+2*x)/((1-x)*(1-2*x)^3).
a(n) = 2^n*(n^2-2*n+3) - 3.
a(n) = Sum_{k=0..n} k^2*2^(k-1). (End)
a(n) = 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4). - Harvey P. Dale, Mar 04 2015
E.g.f.: -3*exp(x) + (3 -2*x +4*x^2)*exp(2*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, 1, 9, 45}, 29] (* Bruno Berselli, Mar 06 2012 *)
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PROG
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(Magma) m:=28; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)/((1-x)*(1-2*x)^3))); // Bruno Berselli, Mar 06 2012
(PARI) for(n=0, 28, print1(2^n*(n^2-2*n+3)-3", ")); \\ Bruno Berselli, Mar 06 2012
(Sage) [2^n*(3-2*n+n^2) -3 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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