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A051662
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House numbers: a(n)=(n+1)^3 + sum(i^2,i=1..n).
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=(n+1)*(8*n^2+13*n+6)/6
Binomial transform of [1, 8, 15, 8, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
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) [From Harvey P. Dale, June 23 2011]
G.f.: (1+5*x+2*x^2)/(x-1)^4 [From Harvey P. Dale, June 23 2011]
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MAPLE
| a:=n->sum(k^2, k=1..n):seq(a(n)+sum(n^2, k=2..n), n=1...40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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MATHEMATICA
| Table[(n+1)^3+Sum[i^2, {i, n}], {n, 0, 40}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 9, 32, 78}, 40] (* From Harvey P. Dale, June 23 2011 *)
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PROG
| (PARI) a(n)=((8*n+21)*n+19)*n/6+1 \\ Charles R Greathouse IV, Jun 23 2011
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CROSSREFS
| A000578(n+1)+A000330(n).
Cf. A000330.
Sequence in context: A063134 A027620 A152619 * A196016 A183426 A061913
Adjacent sequences: A051659 A051660 A051661 * A051663 A051664 A051665
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 01 2006
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 08 2006
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