The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108648 a(n) = (n+1)^2*(n+2)^3*(n+3)/24. 1
 1, 18, 120, 500, 1575, 4116, 9408, 19440, 37125, 66550, 113256, 184548, 289835, 441000, 652800, 943296, 1334313, 1851930, 2527000, 3395700, 4500111, 5888828, 7617600, 9750000, 12358125, 15523326, 19336968, 23901220, 29329875, 35749200 (list; graph; refs; listen; history; text; internal format)
 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 (p. 230, no. 24). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 230, no. 24). Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1). FORMULA From Colin Barker, Apr 22 2020: (Start) G.f.: (1 + 11*x + 15*x^2 + 3*x^3) / (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) for n>6. (End) a(n) = A000217(n+1) * A002415(n+2). - J. M. Bergot, May 21 2022 From Amiram Eldar, May 28 2022: (Start) Sum_{n>=0} 1/a(n) = 24*zeta(3) + 6*Pi^2 - 87. Sum_{n>=0} (-1)^n/a(n) = 99 - Pi^2 - 96*log(2) - 18*zeta(3). (End) MAPLE a:=(n+1)^2*(n+2)^3*(n+3)/24: seq(a(n), n=0..36); PROG (PARI) Vec((1 + 11*x + 15*x^2 + 3*x^3) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Apr 22 2020 CROSSREFS Sequence in context: A044350 A044731 A190705 * A264360 A223046 A037064 Adjacent sequences:  A108645 A108646 A108647 * A108649 A108650 A108651 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 13 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 2 07:50 EDT 2022. Contains 354985 sequences. (Running on oeis4.)