A163416 a(n) = 20*a(n-1) - 98*a(n-2) for n>1, a(0)=1, a(1)=14.

1, 14, 182, 2268, 27524, 328216, 3866968, 45174192, 524520976, 6063348704, 69863918432, 803070195648, 9214739906624, 105593918958976, 1208833868330368, 13828473308627712, 158103747076178176, 1806884557278047744, 20643523932095493632, 235795792028661193728, 2692850495227865498624

Offset

0,2

Comments

Binomial transform of A163415. Tenth binomial transform of A143095.

Links

G. C. Greubel, Table of n, a(n) for n = 0..940

Index entries for linear recurrences with constant coefficients, signature (20, -98).

Formula

a(n) = ((1 + 2*sqrt(2))*(10 + sqrt(2))^n + (1 - 2*sqrt(2))*(10 - sqrt(2))^n)/2.

O.g.f.: (1 - 6*x)/(1 - 20*x + 98*x^2).

E.g.f.: exp(10*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 21 2016

Mathematica

LinearRecurrence[{20, -98}, {1, 14}, 30] (* Harvey P. Dale, Aug 14 2012 *)

Prog

(Magma) [n le 2 select 13*n-12 else 20*Self(n-1)-98*Self(n-2): n in [1..17]];
(PARI) Vec((1-6*x)/(1-20*x+98*x^2) + O(x^50)) \\ G. C. Greubel, Dec 21 2016

Crossrefs

Cf. A163415, A143095.

Sequence in context: A126866 A230055 A133286 * A162783 A199942 A097828

Adjacent sequences: A163413 A163414 A163415 * A163417 A163418 A163419

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 27 2009

Status

approved