A274603 Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers.

45, 4455, 436590, 42781410, 4192141635, 410787098865, 40252943547180, 3944377680524820, 386508759747885225, 37873914077612227275, 3711257070846250387770, 363665319028854925774230, 35635490007756936475486815, 3491914355441150919671933685

Offset: 1

Author

Altug Alkan, Jun 30 2016

Keywords

• nonn
• easy

Comments

Inspired by A274579.

a(n+1) / a(n) goes to 49 + 20*sqrt(6) when n goes to infinity.

Intersection of A045943 and A074377. - Colin Barker, Jun 30 2016

Examples

			45 is a term because 2*45 + 1 = 91 and 3*45 + 1 = 136 are both triangular numbers.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Crossrefs

Cf. A000217, A045943, A074377, A274579.

Programs

PARI

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

PARI

Vec(45*x/((1-x)*(1-98*x+x^2)) + O(x^20)) \\ Colin Barker, Jun 30 2016

Formula

From Colin Barker, Jun 30 2016: (Start)

a(n) = 99*a(n-1)-99*a(n-2)+a(n-3) for n>3.

G.f.: 45*x / ((1-x)*(1-98*x+x^2)).

(End)

Extensions

More terms from Colin Barker, Jun 30 2016