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A025426 Number of partitions of n into 2 nonzero squares. 36
0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 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, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,51

COMMENTS

For records see A007511, A048610, A016032. - R. J. Mathar, Feb 26 2008

LINKS

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

Index entries for sequences related to sums of squares

FORMULA

Let m = A004018(n)/4. If m is even then a(n) = m/2, otherwise a(n) = (m - (-1)^A007814(n))/2. - Max Alekseyev, Mar 09 2009, Mar 14 2009

a(A018825(n)) = 0; a(A000404(n)) > 0; a(A025284(n)) = 1; a(A007692(n)) > 1. - Reinhard Zumkeller, Aug 16 2011

a(A000578(n)) = A084888(n). - Reinhard Zumkeller, Jul 18 2012

MAPLE

A025426 := proc(n)

    local a, x;

    a := 0 ;

    for x from 1 do

        if 2*x^2 > n then

            return a;

        end if;

        if issqr(n-x^2) then

            a := a+1 ;

        end if;

    end do:

end proc: # R. J. Mathar, Sep 15 2015

MATHEMATICA

m[n_] := m[n] = SquaresR[2, n]/4; a[0] = 0; a[n_] := If[ EvenQ[ m[n] ], m[n]/2, (m[n] - (-1)^IntegerExponent[n, 2])/2]; Table[ a[n], {n, 0, 107}] (* Jean-Fran├žois Alcover, Jan 31 2012, after Max Alekseyev *)

PROG

(Haskell)

a025426 n = sum $ map (a010052 . (n -)) $

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

a025426_list = map a025426 [0..]

-- Reinhard Zumkeller, Aug 16 2011

(PARI) a(n)=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 \\ Charles R Greathouse IV, Jan 31 2012

CROSSREFS

Cf. A000161 (2 nonnegative squares), A063725 (order matters), A025427 (3 nonzero squares).

Cf. A172151, A004526. - Reinhard Zumkeller, Jan 26 2010

Column k=2 of A243148.

Sequence in context: A285313 A231366 A158924 * A269244 A204246 A053200

Adjacent sequences:  A025423 A025424 A025425 * A025427 A025428 A025429

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified February 20 10:10 EST 2018. Contains 299384 sequences. (Running on oeis4.)