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1, 13, 94, 526, 2551, 11299, 47020, 186988, 718429, 2686729, 9831658, 35340826, 125154355, 437641663, 1513809688, 5187129880, 17627632249, 59469045061, 199327841590, 664232428390, 2201904349231, 7264715299483, 23865295832644, 78091766836996
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The first differences are in the third row of the square array of A072590.
The general formula for the partial sums of the sequence 1, 4*m, 9*m^2, 16*m^3, 25*m^4,...,n^2*m^(n-1),... is (n^2*m^(n+2)-(2*n*(n+1)-1)*m^(n+1)+(n+1)^2*m^n-m-1)/(m-1)^3 with m>1 (see also References).
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REFERENCES
| "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno) - Apr / May, 1913 - p. 99 (Problem 1277, case x=3).
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LINKS
| Bruno Berselli, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n) = (3^n*(n^2-n+1)-1)/2.
G.f.: x*(1+3*x)/((1-x)*(1-3*x)^3).
a(n) = 10*a(n-1)-36*a(n-2)+54*a(n-3)-27a(n-4) for n>4.
a(n) = 9*A027472(n+1)+A003462(n) for n>2.
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CROSSREFS
| Sequence in context: A005414 A044264 A044645 * A094499 A141894 A160554
Adjacent sequences: A153700 A153701 A153702 * A153704 A153705 A153706
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KEYWORD
| nonn,easy
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AUTHOR
| Bruno Berselli (berselli.bruno(AT)yahoo.it), Dec 12 2010
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