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

1,2

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

Table of n, a(n) for n=1..13.

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

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).

Example

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.

Prog

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

Crossrefs

Cf. A076139, A014979.

Sequence in context: A208404 A208411 A249965 * A232455 A208579 A080691

Adjacent sequences: A108278 A108279 A108280 * A108282 A108283 A108284

Keyword

nonn

Author

Michael Somos, May 30 2005

Status

approved