login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A092362 Number of partitions of n^2 into squares greater than 1. 7
1, 0, 1, 1, 2, 3, 5, 8, 11, 28, 44, 94, 167, 354, 643, 1314, 2412, 4792, 8981, 17374, 32566, 62008, 115702, 217040, 402396, 745795, 1372266, 2517983, 4595652, 8354350, 15125316, 27265107, 48972467, 87584837, 156119631, 277152178, 490437445, 864534950 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = A078134(A000290(n)).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) ~ exp(3*Pi^(1/3) * Zeta(3/2)^(2/3) * n^(2/3) / 2^(4/3)) * Zeta(3/2)^(4/3) / (2^(11/3) * sqrt(3) * Pi^(5/6) * n^(11/3)). - Vaclav Kotesovec, Apr 10 2017

EXAMPLE

a(6) = 5: 6^2 = 36 = 16+16+4 = 16+4+4+4+4+4 = 9+9+9+9 = 4+4+4+4+4+4+4+4+4.

MAPLE

b:=proc(n, i) option remember; `if`(n=0, 1,

     `if`(i<2, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))

   end:

a:= n-> b(n^2, n):

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 15 2013

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, b[n, i-1] + If[i^2>n, 0, b[n-i^2, i]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A001156, A037444.

Cf. A093115, A093116.

Sequence in context: A262841 A334741 A259973 * A105766 A056695 A287006

Adjacent sequences:  A092359 A092360 A092361 * A092363 A092364 A092365

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 19 2004

EXTENSIONS

Corrected a(0) and more terms from Alois P. Heinz, Apr 15 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)