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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
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
J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Azulenoids, MATCH, No. 34, 1996, 91-108.
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: A276235 A334833 A048476 * A256569 A132130 A022571
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 23 2006
STATUS
approved