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 A025426 Number of partitions of n into 2 nonzero squares. 41
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 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 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 a(n) = Sum_{i=1..floor(n/2)} A010052(i) * A010052(n-i). - Wesley Ivan Hurt, Apr 19 2019 a(n) = [x^n y^2] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019 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-François 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,easy AUTHOR STATUS approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)