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A122678 Related to number of n-circum-C_5 H_5 systems. 2
1, 6, 21, 61, 166, 441, 1161, 3046, 7981, 20901, 54726, 143281, 375121, 982086, 2571141, 6731341, 17622886, 46137321, 120789081, 316229926, 827900701, 2167472181, 5674515846, 14856075361, 38893710241, 101825055366, 266581455861, 697919312221, 1827176480806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that the index in Eq. (5) of the paper must be 2k-1, not 2k as published, to reproduce the numbers. - R. J. Mathar, Nov 23 2014

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Azulenoids, MATCH, No. 34, 1996, 91-108.

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

FORMULA

a(n) = 5*Fibonacci(2*k-1)-4 = A106729(k-1)-4.

G.f.: -x*(1+x)^2 / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Nov 23 2014

From Colin Barker, Nov 03 2016: (Start)

a(n) = 2^(-1-n)*(-2^(3+n)-(-5+sqrt(5))*(3+sqrt(5))^n+(3-sqrt(5))^n*(5+sqrt(5))).

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

PROG

(PARI) Vec(-x*(1+x)^2/((x-1)*(x^2-3*x+1)) + O(x^40)) \\ Colin Barker, Nov 03 2016

CROSSREFS

Sequence in context: A012593 A276235 A048476 * A256569 A132130 A022571

Adjacent sequences:  A122675 A122676 A122677 * A122679 A122680 A122681

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 23 2006

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)