A108281 Numbers that are both triangular and pentagonal of the second kind.

0, 15, 2926, 567645, 110120220, 21362755051, 4144264359690, 803965923024825, 155965244802456376, 30256453525753512135, 5869596018751378897830, 1138671371184241752666901, 220896376413724148638480980

Offset: 1

Author

Michael Somos, May 30 2005

Keywords

• nonn

Examples

			15*x^2 + 2926*x^3 + 567645*x^4 + 110120220*x^5 + 21362755051*x^6 + ...
a(4) = 567645 which is 1065*(1065-1)/2 = 615*(3*615+1)/2.
		

References

• L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 22.

Links

• Index entries for linear recurrences with constant coefficients, signature (195, -195, 1).

Crossrefs

Cf. A076139, A014979.

Programs

PARI

{a(n) = polchebyshev( 2*n - 2, 2, 7) / 14 + polchebyshev( 2*n - 2, 1, 7) / 84 - 1 / 12} /* Michael Somos, Jun 16 2011 */

Formula

a(n) = 194 * a(n-1) - a(n-2) + 16.

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

a(n) = A076139(2*n - 2) = A014979(2 - n).