OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 167-169, Table 10.5/II/3).
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: (1 + 5*x + 3*x^2)/(1-x)^7.
a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 03 2015
From Amiram Eldar, Jun 02 2022: (Start)
Sum_{n>=0} 1/a(n) = 405*sqrt(3)*Pi/7 + 20*Pi^2 - 3645*log(3)/7 + 1280/21.
Sum_{n>=0} (-1)^n/a(n) = 810*sqrt(3)*Pi/7 - 10*Pi^2 - 4160*log(2)/7 - 2480/21. (End)
MAPLE
a:=n->(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240: seq(a(n), n=0..35);
MATHEMATICA
CoefficientList[Series[(1+5x+3x^2)/(1-x)^7, {x, 0, 40}], x] (* Harvey P. Dale, Feb 19 2011 *)
Table[(n + 1) (n + 2)^2 (n + 3) (n + 4) (3 n + 5) / 240, {n, 0, 50}] (* Vincenzo Librandi, May 03 2015 *)
PROG
(Magma) [(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240 : n in [0..50]]; // Wesley Ivan Hurt, May 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 18 2005
STATUS
approved