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A110693
Kekulé numbers for certain benzenoids.
1
1, 36, 448, 3175, 15786, 61446, 199872, 566676, 1441275, 3356782, 7268976, 14805583, 28621684, 52892100, 93977088, 161303616, 268510869, 434915472, 687359200, 1062509679, 1609692766, 2394343930, 3502175040, 5044162500
OFFSET
0,2
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 243, H*(3,5,n)).
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = 2*(n+1)*(n+2)^3*(n+3)*(n+4)*(25*n^3 + 142*n^2 + 295*n + 210)/8!.
G.f.: ( 1+26*x+133*x^2+195*x^3+86*x^4+9*x^5 )/(1-x)^10. - R. J. Mathar, Nov 01 2015
MAPLE
a:=n->(n+1)*(n+2)^3*(n+3)*(n+4)*(25*n^3+142*n^2+295*n+210)/20160: seq(a(n), n=0..27);
MATHEMATICA
CoefficientList[Series[(1+26*x+133*x^2+195*x^3+86*x^4+9*x^5)/(1-x)^10, {x, 0, 50}], x] (* G. C. Greubel, Sep 06 2017 *)
PROG
(Python)
A110693_list, m = [], [450, -816, 508, -121, 10, 1, 1, 1, 1, 1]
for _ in range(10001):
A110693_list.append(m[-1])
for i in range(9):
m[i+1] += m[i] # Chai Wah Wu, Jun 12 2016
(PARI) x='x+O(x^50); Vec((1+26*x+133*x^2+195*x^3+86*x^4+9*x^5)/(1-x)^10) \\ G. C. Greubel, Sep 06 2017
CROSSREFS
Sequence in context: A281403 A256149 A244498 * A104671 A323549 A128986
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 03 2005
STATUS
approved