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A122679 Related to number of n-circum-C_5 H_5 systems. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A147114 A296669

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

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)