login
A225839
Triangular numbers representable as triangular(m) + triangular(2m).
1
0, 378, 17766, 39209940, 1842032556, 4065365016846, 190985619471570, 421505175637435176, 19801770996209306328, 43702499616375188919330, 2053087220237987679246270, 4531162564803507161896556028, 212868189148913267563402477956, 469799997000254729943383533193910
OFFSET
1,2
COMMENTS
Triangular numbers of the sequence A147875: a(n) = A147875(A225785(n)) - see also Ralf Stephan in Program lines. [Bruno Berselli, May 20 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]
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 *)
PROG
(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
CROSSREFS
Cf. A108281 (triangular numbers representable as triangular(m) + m^2).
Cf. A225785 (numbers n such that triangular(n) + triangular(2n) is a triangular number).
Sequence in context: A235544 A325848 A248915 * A221803 A289347 A171115
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, May 17 2013
EXTENSIONS
More terms from Bruno Berselli, May 20 2013
STATUS
approved