login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167700 Number of partitions of n into distinct odd squares. 11
1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A167701 and A167702 give record values and where they occur: A167701(n)=a(A167702(n)) and a(m) < A167701(n) for m < A167702(n);

a(A167703(n)) = 0.

LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares.

Vaclav Kotesovec, Graph - The asymptotic ratio

FORMULA

a(n) = f(n,1,8) with f(x,y,z) = if x<y then 0^x else f(x-y,y+z,z+8) + f(x,y+z,z+8).

G.f.: Product_{k>=0} (1 + x^((2*k+1)^2)). - Ilya Gutkovskiy, Jan 11 2017

a(n) ~ exp(3 * 2^(-7/3) * Pi^(1/3) * (sqrt(2)-1)^(2/3) * Zeta(3/2)^(2/3) * n^(1/3)) * (sqrt(2)-1)^(1/3) * Zeta(3/2)^(1/3) / (2^(7/6) * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, Sep 18 2017

EXAMPLE

a(50) = #{49+1} = 1;

a(130) = #{121+9, 81+49} = 2.

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[1 + x^((2*k-1)^2), {k, 1, Floor[Sqrt[nmax]/2] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 18 2017 *)

PROG

(Haskell)

a167700 = p a016754_list where

   p _  0 = 1

   p (q:qs) m = if m < q then 0 else p qs (m - q) + p qs m

-- Reinhard Zumkeller, Mar 15 2014

CROSSREFS

Cf. A033461, A016754, A167661, A000700, A111900.

Sequence in context: A016373 A281815 A205988 * A010057 A204220 A281814

Adjacent sequences:  A167697 A167698 A167699 * A167701 A167702 A167703

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Nov 09 2009

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 September 17 09:02 EDT 2019. Contains 327128 sequences. (Running on oeis4.)