A129345 a(2n) = A001542(n+1), a(2n+1) = A038761(n+1); a Pellian-related sequence.

2, 9, 12, 53, 70, 309, 408, 1801, 2378, 10497, 13860, 61181, 80782, 356589, 470832, 2078353, 2744210, 12113529, 15994428, 70602821, 93222358, 411503397, 543339720, 2398417561, 3166815962, 13979001969, 18457556052, 81475594253, 107578520350, 474874563549

Offset

0,1

Comments

Summation of -a(n) and A129346 returns twice Pell numbers A000129 (apart from signs; starting from 2nd term of A000129).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

Formula

G.f.: (2+9*x-x^3)/((x^2+2*x-1)*(x^2-2*x-1)).

From Colin Barker, May 26 2016: (Start)

a(n) = ((-1-sqrt(2))^(1+n)-(-1+sqrt(2))^(1+n)+(1-sqrt(2))^n*(-4+3*sqrt(2))+(1+sqrt(2))^n*(4+3*sqrt(2)))/(2*sqrt(2)).

a(n) = 6*a(n-2)-a(n-4) for n>3.

(End)

Mathematica

CoefficientList[Series[(2 + 9 x - x^3)/((x^2 + 2 x - 1) (x^2 - 2 x - 1)), {x, 0, 29}], x] (* Michael De Vlieger, May 26 2016 *)

Prog

(PARI) Vec((2+9*x-x^3)/((x^2+2*x-1)*(x^2-2*x-1)) + O(x^40)) \\ Colin Barker, May 26 2016

Crossrefs

Cf. A129346, A000129, A001542, A038761.

Sequence in context: A324571 A076505 A218073 * A216350 A125019 A259984

Adjacent sequences: A129342 A129343 A129344 * A129346 A129347 A129348

Keyword

easy,nonn

Author

Creighton Dement, Apr 10 2007

Status

approved