A122678 Related to number of n-circum-C_5 H_5 systems.

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

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: A276235 A334833 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