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 A053603 Number of ways to write n as an ordered sum of two nonzero triangular numbers. 5
 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 2, 1, 2, 0, 0, 4, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 3, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 2, 3, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 3, 2, 0, 0, 4, 0, 0, 2, 0, 6, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(A051611(n)) = 0; A051533(a(n)) > 0. - Reinhard Zumkeller, Jun 27 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA G.f.: ( Sum_{k>=1} x^(k*(k+1)/2) )^2. - Ilya Gutkovskiy, Dec 24 2016 MATHEMATICA nmax = 100; m0 = 10; A053603 := Table[a[n], {n, 0, nmax}]; Clear[counts]; counts[m_] := counts[m] = (Clear[a]; a[_] = 0; Do[k = i*(i+1)/2 + j*(j+1)/2; a[k] = a[k]+1, {i, 1, m}, {j, 1, m}]; A053603); counts[m = m0]; counts[m = 2*m]; While[ counts[m] != counts[m/2], m = 2*m]; A053603 (* Jean-François Alcover, Sep 05 2013 *) PROG (Haskell) a053603 n = sum \$ map (a010054 . (n -)) \$                   takeWhile (< n) \$ tail a000217_list -- Reinhard Zumkeller, Jun 27 2013 (PARI) istriang(n)={n>0 && issquare(8*n+1); } a(n) = { my(t=1, ct=0, j=1); while (t

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Last modified December 15 20:49 EST 2018. Contains 318154 sequences. (Running on oeis4.)