A274680 Values of n such that 2*n+1 and 4*n+1 are both triangular numbers.

0, 16065, 545751, 21394547226, 726784809030, 28491418065071115, 967869505172593485, 37942420317086720855700, 1288925370210688376036076, 50528452330120333959563160501, 1716479960463788790499334882595, 67289447366315927998308608003134830

Offset: 1

Author

Colin Barker, Jul 02 2016

Keywords

• nonn
• easy

Examples

			16065 is in the sequence because 2*16065+1 = 32131, 4*16065+1 = 64261, and 32131 and 64261 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..325
• Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).

Crossrefs

Cf. A124174 (2*n+1 and 9*n+1), A274579 (2*n+1 and 5*n+1), A274603 (2*n+1 and 3*n+1).

Programs

Mathematica

Rest@ CoefficientList[Series[459 x^2 (35 + 1154 x + 35 x^2)/((1 - x) (1 - 1154 x + x^2) (1 + 1154 x + x^2)), {x, 0, 12}], x] (* Michael De Vlieger, Jul 02 2016 *)

PARI

isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(4*n+1, 3)

PARI

concat(0, Vec(459*x^2*(35+1154*x+35*x^2)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)) + O(x^20)))

Formula

Intersection of A074377 and A274681.

G.f.: 459*x^2*(35+1154*x+35*x^2) / ((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)).