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A051662
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House numbers: a(n) = (n+1)^3 + Sum_{i=1..n} i^2.
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9
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1, 9, 32, 78, 155, 271, 434, 652, 933, 1285, 1716, 2234, 2847, 3563, 4390, 5336, 6409, 7617, 8968, 10470, 12131, 13959, 15962, 18148, 20525, 23101, 25884, 28882, 32103, 35555, 39246, 43184, 47377, 51833, 56560, 61566, 66859, 72447, 78338, 84540
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OFFSET
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0,2
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COMMENTS
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Binomial transform of [1, 8, 15, 8, 0, 0, 0, ...]. - Gary W. Adamson, Nov 23 2007
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LINKS
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FORMULA
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a(n) = (n+1)*(8*n^2 + 13*n + 6)/6.
a(0)=1, a(1)=9, a(2)=32, a(3)=78, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Jun 23 2011
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MAPLE
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a:=n->sum(k^2, k=1..n):seq(a(n)+sum(n^2, k=2..n), n=1...40); # Zerinvary Lajos, Jun 11 2008
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MATHEMATICA
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Table[(n+1)^3+Sum[i^2, {i, n}], {n, 0, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 9, 32, 78}, 40] (* Harvey P. Dale, Jun 23 2011 *)
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PROG
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(Haskell) - following Gary W. Adamson's comment.
a051662 = sum . zipWith (*) [1, 8, 15, 8] . a007318_row
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CROSSREFS
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Cf. A000330, A220084 (for a list of numbers of the form n*P(k,n)-(n-1)*P(k,n-1), where P(k,n) is the n-th k-gonal pyramidal number).
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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EXTENSIONS
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Corrected by T. D. Noe, Nov 01 2006 and Nov 08 2006
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STATUS
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approved
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