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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-Fran├žois 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<n, ct+=istriang(n-t); j+=1; t+=j; ); ct; }

\\ Joerg Arndt, Sep 05 2013

CROSSREFS

Cf. A000217, A007294, A051611, A051533, A052343-A052348, A053604.

Cf. A010054.

Sequence in context: A264394 A283310 A035445 * A085794 A239002 A004548

Adjacent sequences:  A053600 A053601 A053602 * A053604 A053605 A053606

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 20 2000

STATUS

approved

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