A122679 Related to number of n-circum-C_5 H_5 systems.

0, 5, 25, 80, 225, 605, 1600, 4205, 11025, 28880, 75625, 198005, 518400, 1357205, 3553225, 9302480, 24354225, 63760205, 166926400, 437019005, 1144130625, 2995372880, 7841988025, 20530591205, 53749785600, 140718765605, 368406511225, 964500768080

Offset

1,2

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) = 15*Fibonacci(2*k-1)-5*Fibonacci(2*k)-10 = 5*A004146(n-1).

G.f.: -5*x^2*(1+x) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Nov 23 2014

a(1)=0, a(2)=5, a(3)=25, a(n) = 4*a(n-1)-4*a(n-2)+a(n-3). - Harvey P. Dale, Apr 21 2015

a(n) = -5*2^(-1-n)*(2^(2+n)-(3-sqrt(5))^n*(3+sqrt(5))+(-3+sqrt(5))*(3+sqrt(5))^n). - Colin Barker, Nov 03 2016

Mathematica

LinearRecurrence[{4, -4, 1}, {0, 5, 25}, 40] (* Harvey P. Dale, Apr 21 2015 *)

Prog

(PARI) concat(0, Vec(-5*x^2*(1+x)/((x-1)*(x^2-3*x+1)) + O(x^40))) \\ Colin Barker, Nov 03 2016

Crossrefs

Sequence in context: A243303 A238449 A062989 * A264132 A355949 A147114

Adjacent sequences: A122676 A122677 A122678 * A122680 A122681 A122682

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 23 2006

Extensions

More terms from Harvey P. Dale, Apr 21 2015

Status

approved