A274832 Values of n such that 2*n+1 and 7*n+1 are both triangular numbers (A000217).

0, 27, 297, 24570, 267030, 22064157, 239792967, 19813588740, 215333817660, 17792580624687, 193369528466037, 15977717587380510, 173645621228683890, 14347972600887073617, 155933574493829667507, 12884463417879004727880, 140028176249837812737720

Offset: 1

Author

Colin Barker, Jul 08 2016

Keywords

• nonn
• easy

Comments

Intersection of A074377 and A274830.

Examples

			27 is in the sequence because 2*27+1 = 55, 7*27+1 = 190, and 55 and 190 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..650
• Index entries for linear recurrences with constant coefficients, signature (1,898,-898,-1,1).

Crossrefs

Cf. A000217, A074377, A274830.

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), A274680 (2*n+1 and 4*n+1), A274756 (2*n+1 and 7*n+1).

Programs

Mathematica

LinearRecurrence[{1, 898, -898, -1, 1}, {0, 27, 297, 24570, 267030}, 20] (* Paolo Xausa, Oct 21 2024 *)

PARI

isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(7*n+1, 3)

PARI

concat(0, Vec(27*x^2*(1+10*x+x^2)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20)))

Formula

G.f.: 27*x^2*(1+10*x+x^2) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).