A225839 Triangular numbers representable as triangular(m) + triangular(2m).

0, 378, 17766, 39209940, 1842032556, 4065365016846, 190985619471570, 421505175637435176, 19801770996209306328, 43702499616375188919330, 2053087220237987679246270, 4531162564803507161896556028, 212868189148913267563402477956, 469799997000254729943383533193910

Offset: 1

Author

Alex Ratushnyak, May 17 2013

Keywords

• nonn
• easy

Comments

Triangular numbers of the sequence A147875: a(n) = A147875(A225785(n)) - see also Ralf Stephan in Program lines. [Bruno Berselli, May 20 2013]

Links

• Index entries for linear recurrences with constant coefficients, signature (1,103682,-103682,-1,1).

Crossrefs

Cf. A000217, A147875.

Cf. A108281 (triangular numbers representable as triangular(m) + m^2).

Cf. A225785 (numbers n such that triangular(n) + triangular(2n) is a triangular number).

Programs

Mathematica

CoefficientList[Series[378 x (1 + 46 x + x^2)/((1 - x) (1 - 322 x + x^2) (1 + 322 x + x^2)), {x, 0, 20}], x] (* Bruno Berselli, May 20 2013 *)
LinearRecurrence[{1,103682,-103682,-1,1},{0,378,17766,39209940,1842032556},20] (* Harvey P. Dale, Jan 16 2019 *)

PARI

for(n=1,10^9,t=n*(5*n+3)/2;x=sqrtint(2*t);if(t==x*(x+1)/2,print(t))) \\ Ralf Stephan, May 17 2013

Formula

G.f.: 378*x*(1+46*x+x^2)/((1-x)*(1-322*x+x^2)*(1+322*x+x^2)). [Bruno Berselli, May 20 2013]

Extensions

More terms from Bruno Berselli, May 20 2013