This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108680 KekulĂ© numbers for certain benzenoids. 1
 1, 18, 140, 700, 2646, 8232, 22176, 53460, 117975, 242242, 468468, 861224, 1516060, 2570400, 4217088, 6720984, 10439037, 15844290, 23554300, 34364484, 49286930, 69595240, 96876000, 133087500, 180626355, 242402706, 321924708, 423393040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 232, # 3). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA G.f.: (1 + 9*x + 14*x^2 + 4*x^3)/(1 - x)^9. a(n) = (n + 1)*(n + 2)^3*(n + 3)^2*(n + 4)*(n + 5)/1440 (from Maple section). Sum_{n>=0} 1/a(n) = -240*zeta(3) + (400/3)*Pi^2 - 18475/18. - Jaume Oliver Lafont, Jul 10 2017 MAPLE a:=n->(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: seq(a(n), n=0..30); MATHEMATICA CoefficientList[Series[(1 + 9 x + 14 x^2 + 4 x^3) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 11 2017 *) PROG (MAGMA) [(n+1)*(n+2)^3*(n+3)^2*(n+4)*(n+5)/1440: n in [0..30]]; // Vincenzo Librandi, Jul 11 20217 CROSSREFS Sequence in context: A087115 A163707 A212154 * A204273 A081074 A299062 Adjacent sequences:  A108677 A108678 A108679 * A108681 A108682 A108683 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 18 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)