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A114647 Expansion of (-3+4*x+3*x^2)/((1-x)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence. 5
3, 2, 7, 12, 31, 70, 171, 408, 987, 2378, 5743, 13860, 33463, 80782, 195027, 470832, 1136691, 2744210, 6625111, 15994428, 38613967, 93222358, 225058683, 543339720, 1311738123, 3166815962, 7645370047, 18457556052, 44560482151, 107578520350, 259717522851 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Generating floretion: - 1.5'i + 'j + 'k - .5i' + j' + k' + .5'ii' - .5'jj' - .5'kk' - 'ij' + 'ik' - 'ji' + .5'jk' + 2'ki' - .5'kj' + .5e

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).

FORMULA

a(n) = A000129(n+1)+2*A059841(n). - R. J. Mathar, Nov 10 2009

From Colin Barker, May 26 2016: (Start)

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

a(n) = 2*a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4) for n>3.

(End)

PROG

(PARI) Vec((-3+4*x+3*x^2)/((1-x)*(x+1)*(x^2+2*x-1)) + O(x^50)) \\ Colin Barker, May 26 2016

CROSSREFS

Cf. A100828, A114688, A114689, A114695, A114696, A114697, A000129.

Sequence in context: A143332 A255919 A212189 * A234750 A052546 A260016

Adjacent sequences:  A114644 A114645 A114646 * A114648 A114649 A114650

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Feb 18 2006

STATUS

approved

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Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.