A274579 Values of k such that 2*k+1 and 5*k+1 are both triangular numbers.

0, 1, 7, 27, 540, 2002, 10660, 39501, 779247, 2887450, 15372280, 56960982, 1123674201, 4163701465, 22166817667, 82137697110, 1620337419162, 6004054625647, 31964535704101, 118442502272205, 2336525434757970, 8657842606482076, 46092838318496542

Offset: 1

Author

Colin Barker, Jun 29 2016

Keywords

• nonn
• easy

Comments

Intersection of A074377 and A085787.

Examples

			7 is in the sequence because 2*7+1 = 15, 5*7+1 = 36, and 15 and 36 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1442,-1442,0,0,-1,1).

Crossrefs

Cf. A000217, A074377, A085787, A124174.

Programs

PARI

concat(0, Vec(x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6)/((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)) + O(x^30)))

PARI

isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(5*n+1, 3); \\ Michel Marcus, Jun 29 2016

Formula

G.f.: x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6) / ((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)).