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A112524
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a(1)=1; a(n) = a(n-1) + 2*n^2.
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1
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1, 9, 27, 59, 109, 181, 279, 407, 569, 769, 1011, 1299, 1637, 2029, 2479, 2991, 3569, 4217, 4939, 5739, 6621, 7589, 8647, 9799, 11049, 12401, 13859, 15427, 17109, 18909, 20831, 22879, 25057, 27369, 29819, 32411, 35149, 38037, 41079, 44279, 47641
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OFFSET
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1,2
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COMMENTS
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This is the total number of operations or total storage if a process first replaces a square array by an array one smaller, repeatedly down to 1 and then regrows the array to the original size.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Lewis Carrol Determinant Formula
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FORMULA
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Twice the sum of the first n square numbers - 1 = n*(n + 1)*(2n + 1)/3 - 1 - Stefan Steinerberger, Mar 11 2006
G.f.: x(1+5x-3x^2+x^3)/(1-x)^4. a(n)=A006331(n)-1. [From R. J. Mathar, Sep 09 2008]
a(1)=1, a(2)=9, a(3)=27, a(4)=59, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Dec 03 2012
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MAPLE
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a[1]:=1: for n from 2 to 50 do a[n]:=a[n-1]+2*n^2 od: seq(a[n], n=1..50); - Emeric Deutsch, Feb 13 2006
a:=n->sum(k^2, k=1..n):seq(a(n)+sum(k^2, k=2..n), n=1...40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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MATHEMATICA
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Table[n*(n + 1)*(2n + 1)/3 - 1, {n, 1, 50}] - Stefan Steinerberger, Mar 11 2006
2*Accumulate[Range[50]^2]-1 (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 9, 27, 59}, 50] (* Harvey P. Dale, Dec 03 2012 *)
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CROSSREFS
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Sequence in context: A051412 A027468 A158926 * A153237 A011923 A029875
Adjacent sequences: A112521 A112522 A112523 * A112525 A112526 A112527
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KEYWORD
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easy,nonn
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AUTHOR
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Dennis Farr (dfarr(AT)comcast.net), Dec 13 2005
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EXTENSIONS
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Definition corrected by Alexandre Wajnberg, Jan 02 2006
More terms from Emeric Deutsch, Feb 13 2006
More terms from Stefan Steinerberger, Mar 11 2006
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STATUS
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approved
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