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A368528
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a(n) = Sum_{k=1..n} k^2 * 3^(n-k).
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1
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0, 1, 7, 30, 106, 343, 1065, 3244, 9796, 29469, 88507, 265642, 797070, 2391379, 7174333, 21523224, 64569928, 193710073, 581130543, 1743391990, 5230176370, 15690529551, 47071589137, 141214767940, 423644304396, 1270932913813, 3812798742115
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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+x)/((1-3*x) * (1-x)^3).
a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).
a(n) = (3^(n+1) - (n^2 + 3*n + 3))/2.
a(0) = 0; a(n) = 3*a(n-1) + n^2.
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PROG
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(PARI) a(n) = sum(k=1, n, k^2*3^(n-k));
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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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