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 A112524 a(1)=1; a(n) = a(n-1) + 2*n^2. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Lewis Carrol Determinant Formula Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA 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. - 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 MAPLE 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 MATHEMATICA 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 *) CROSSREFS Sequence in context: A051412 A027468 A158926 * A254622 A271990 A153237 Adjacent sequences:  A112521 A112522 A112523 * A112525 A112526 A112527 KEYWORD easy,nonn AUTHOR Dennis Farr (dfarr(AT)comcast.net), Dec 13 2005 EXTENSIONS Definition corrected by Alexandre Wajnberg, Jan 02 2006 More terms from Emeric Deutsch, Feb 13 2006 More terms from Stefan Steinerberger, Mar 11 2006 STATUS approved

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Last modified August 7 04:39 EDT 2020. Contains 336274 sequences. (Running on oeis4.)