A274756 Values of n such that 2*n+1 and 6*n+1 are both triangular numbers.

0, 945, 13167, 35578242, 495540990, 1338951572595, 18649189618605, 50390103447476100, 701843601611053692, 1896381151803363988917, 26413182084381205040235, 71368408216577696911440390, 994033693861758668873164410, 2685878672926303893761783662455

Offset: 1

Author

Colin Barker, Jul 04 2016

Keywords

• nonn
• easy

Comments

Intersection of A074377 and A274757.

Examples

			945 is in the sequence because 2*945+1 = 1891, 6*945+1 = 5671, and 1891 and 5671 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..400
• Index entries for linear recurrences with constant coefficients, signature (1,37634,-37634,-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), A274680 (2*n+1 and 4*n+1).

Programs

PARI

isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(6*n+1, 3)

PARI

concat(0, Vec(63*x^2*(15+194*x+15*x^2)/((1-x)*(1-194*x+x^2)*(1+194*x+x^2)) + O(x^20)))

Formula

G.f.: 63*x^2*(15+194*x+15*x^2) / ((1-x)*(1-194*x+x^2)*(1+194*x+x^2)).

a(n) = a(n-1)+37634*a(n-2)-37634*a(n-3)-a(n-4)+a(n-5). - Wesley Ivan Hurt, Apr 24 2021