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A112524
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a(n) = a(n-1) + 2*n^2 with a(1) = 1.
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2
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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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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 +5*x -3*x^2 +x^3)/(1-x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), a(1)=1, a(2)=9, a(3)=27, a(4)=59. - Harvey P. Dale, Dec 03 2012
E.g.f.: ( 3 + (-3 + 6*x + 9*x^2 + 2*x^3)*exp(x) )/3. - G. C. Greubel, Jan 12 2022
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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, Jun 11 2008
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MATHEMATICA
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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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PROG
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(Sage) [n*(n+1)*(2*n+1)/3 - 1 for n in (1..40)] # G. C. Greubel, Jan 12 2022
(Magma) [n*(n+1)*(2*n+1)/3 - 1: n in [1..40]]; // G. C. Greubel, Jan 12 2022
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CROSSREFS
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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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STATUS
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approved
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