A249164 Numbers n such that the triangular number T(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.

1, 3, 113, 331, 11121, 32483, 1089793, 3183051, 106788641, 311906563, 10464197073, 30563660171, 1025384524561, 2994926790243, 100477219209953, 293472261783691, 9845742098050881, 28757286728011523, 964782248389776433, 2817920627083345611, 94538814600100039601

Offset: 1

Author

Colin Barker, Dec 15 2014

Keywords

• nonn
• easy

Comments

Also nonnegative integers y in the solutions to 6*x^2-y^2+4*x-y+2 = 0, the corresponding values of x being A122513.

Examples

			113 is in the sequence because T(113) = 6441 = 3151+3290 = P(46)+P(47).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Crossrefs

Cf. A000217, A000326, A122513.

Programs

PARI

Vec(-x*(x+1)^2*(11*x^2+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x+1)^2*(11*x^2+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).