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A025441 Number of partitions of n into 2 distinct nonzero squares. 17
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,66

LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000

Michael Gilleland, Some Self-Similar Integer Sequences

Index entries for sequences related to sums of squares

FORMULA

a(A025302(n)) = 1. - Reinhard Zumkeller, Dec 20 2013

a(n) = Sum_{ m: m^2|n } A157228(n/m^2). - Andrey Zabolotskiy, May 07 2018

a(n) = [x^n y^2] Product_{k>=1} (1 + y*x^(k^2)). - Ilya Gutkovskiy, Apr 22 2019

MAPLE

P:=proc(n) local a, x; a:=1; x:=0; while a^2<trunc(n/2)

do if frac(sqrt(n-a^2))=0 then x:=x+1; fi; a:=a+1; od; x; end:

seq(P(i), i=1..100); # Paolo P. Lava, Mar 12 2018

MATHEMATICA

Table[Count[PowersRepresentations[n, 2, 2], pr_ /; Unequal @@ pr && FreeQ[pr, 0]], {n, 0, 107}] (* Jean-Fran├žois Alcover, Mar 01 2019 *)

PROG

(Haskell)

a025441 n = sum $ map (a010052 . (n -)) $

                      takeWhile (< n `div` 2) $ tail a000290_list

-- Reinhard Zumkeller, Dec 20 2013

(PARI) a(n)=if(n>4, sum(k=1, sqrtint((n-1)\2), issquare(n-k^2)), 0) \\ Charles R Greathouse IV, Jun 10 2016

(PARI) a(n)=if(n<5, return(0)); my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f[, 1], if(f[i, 1]%4==1, t*=f[i, 2]+1, if(f[i, 2]%2, return(0)))); if(t%2, t-(-1)^v, t)/2-issquare(n/2) \\ Charles R Greathouse IV, Jun 10 2016

CROSSREFS

Cf. A060306 gives records; A052199 gives where records occur.

Cf. A000161, A000290, A010052, A025435, A157228, A053866, A145393.

Sequence in context: A088534 A178602 A216279 * A286813 A176891 A219486

Adjacent sequences:  A025438 A025439 A025440 * A025442 A025443 A025444

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 21 03:05 EDT 2019. Contains 323434 sequences. (Running on oeis4.)