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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A025435 Number of partitions of n into 2 distinct squares. 7
0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,26

COMMENTS

a(A004435(n)) = 0; a(A001983(n)) > 0. - Reinhard Zumkeller, Dec 20 2013

LINKS

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

FORMULA

a(n) = A000161(n) - A010052(2n). - M. F. Hasler, Aug 05 2018

EXAMPLE

G.f. = x + x^4 + x^5 + x^9 + x^10 + x^13 + x^16 + x^17 + x^20 + 2*x^25 + ...

MAPLE

A025435 := proc(n)

    local i, j, ans;

    ans := 0;

    for i from 0 to n do

        for j from i+1 to n do

            if i^2+j^2=n then

                ans := ans+1

            fi

        end do

    end do;

    ans ;

end proc: # R. J. Mathar, Aug 04 2018

MATHEMATICA

a[ n_] := If[ n < 0, 0, Sum[ Boole[ n == i^2 + j^2], {i, Sqrt[n]}, {j, 0, i - 1}]]; (* Michael Somos, Jun 24 2015 *)

a[ n_] := Length@ PowersRepresentations[ n, 2, 2] - Boole @ IntegerQ @ Sqrt[2 n]; (* Michael Somos, Jun 24 2015 *)

a[ n_] := SeriesCoefficient[ With[ {f = (EllipticTheta[ 3, 0, x] + 1)/2, g = (EllipticTheta[ 3, 0, x^2] + 1)/2}, f f - g] / 2, {x, 0, n}]; (* Michael Somos, Jun 24 2015 *)

PROG

(Haskell)

a025435 0 = 0

a025435 n = a010052 n + sum

   (map (a010052 . (n -)) $ takeWhile (< n `div` 2) $ tail a000290_list)

-- Reinhard Zumkeller, Dec 20 2013

(PARI) {a(n) = if( n<0, 0, sum(i=1, sqrtint(n), sum(j=0, i-1, n == i^2 + j^2)))}; /* Michael Somos, Jun 24 2015 */

(PARI) A025435(n)=sum(k=sqrtint((n-1+!n)\2)+1, sqrtint(n), issquare(n-k^2))-issquare(n/2) \\ or A000161(n)-issquare(n/2). - M. F. Hasler, Aug 05 2018

CROSSREFS

Cf. A010052, A000290, A000161, A025441.

Sequence in context: A286562 A185644 A319080 * A304685 A186714 A160382

Adjacent sequences:  A025432 A025433 A025434 * A025436 A025437 A025438

KEYWORD

nonn

AUTHOR

David W. Wilson

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 December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)