OFFSET
0,1
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 (p. 311).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: 20*(49 + 1385*z + 4539*z^2 + 2771*z^3 + 256*z^4)/(1-z)^7.
E.g.f.: 10*(98 + 3358*x + 12199*x^2 + 11919*x^3 + 4199*x^4 + 570*x^5 + 25*x^6)*exp(x). - G. C. Greubel, Feb 09 2020
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, Aug 19 2022
MAPLE
a:=n->10*(n+1)^3*(n+2)*(5*n+7)^2: seq(a(n), n=0..30);
MATHEMATICA
Table[10(n+1)^3(n+2)(5n+7)^2, {n, 0, 30}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {980, 34560, 312120, 1548800, 5467500, 15482880, 37565360}, 30] (* Harvey P. Dale, Jan 20 2024 *)
PROG
(PARI) vector(31, n, my(m=n-1); 10*(m+1)^3*(m+2)*(5*m+7)^2) \\ G. C. Greubel, Feb 09 2020
(Magma) [10*(n+1)^3*(n+2)*(5*n+7)^2: n in [0..30]]; // G. C. Greubel, Feb 09 2020
(Sage) [10*(n+1)^3*(n+2)*(5*n+7)^2 for n in (0..30)] # G. C. Greubel, Feb 09 2020
(GAP) List([0..30], n-> 10*(n+1)^3*(n+2)*(5*n+7)^2 ); # G. C. Greubel, Feb 09 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 19 2005
STATUS
approved