A112524 a(n) = a(n-1) + 2*n^2 with a(1) = 1.

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

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, Condensation

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

From R. J. Mathar, Sep 09 2008: (Start)

G.f.: x*(1 +5*x -3*x^2 +x^3)/(1-x)^4.

a(n) = A006331(n) - 1. (End)

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

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, 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 *)

Prog

(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

Crossrefs

Cf. A006331.

Sequence in context: A051412 A027468 A158926 * A254622 A374976 A340119

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