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

1,2

Comments

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.

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).

Formula

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)).

Example

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

Prog

(PARI) 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))

Crossrefs

Cf. A000326, A000384, A122513.

Sequence in context: A264939 A201217 A041391 * A189057 A229015 A324318

Adjacent sequences: A245780 A245781 A245782 * A245784 A245785 A245786

Keyword

nonn,easy

Author

Colin Barker, Dec 15 2014

Status

approved