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A129345 a(2n) = A001542(n+1), a(2n+1) = A038761(n+1); a Pellian-related sequence. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A102237 A076505 A218073 * A216350 A125019 A259984

Adjacent sequences:  A129342 A129343 A129344 * A129346 A129347 A129348

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Apr 10 2007

STATUS

approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)