A122513 -id:A122513 - cp's OEIS frontend

A245783 Numbers n such that the hexagonal number H(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.

1, 2, 57, 166, 5561, 16242, 544897, 1591526, 53394321, 155953282, 5232098537, 15281830086, 512692262281, 1497463395122, 50238609604977, 146736130891846, 4922871049025441, 14378643364005762, 482391124194888217, 1408960313541672806, 47269407300050019801

Offset: 1

Colin Barker, Dec 15 2014

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

			57 is in the sequence because H(57) = 6441 = 3151+3290 = P(46)+P(47).

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).

Cf. A000326, A000384, A122513.

Vec(-x*(6*x^4+11*x^3-43*x^2+x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

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

G.f.: -x*(6*x^4+11*x^3-43*x^2+x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

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.

Original entry on oeis.org

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

Offset: 1

Colin Barker, Dec 15 2014

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.

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

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).

Cf. A000217, A000326, A122513.

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

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)).

cp's OEIS Frontend

A245783 Numbers n such that the hexagonal number H(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula