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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 May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)