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 A053603 Number of ways to write n as an ordered sum of two nonzero triangular numbers. 13
 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 July 24 15:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)