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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A107959 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2 + 5*n + 5)/720. 1
 1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835, 412126, 806806, 1498861, 2662660, 4550560, 7518624, 12058236, 18834453, 28731990, 42909790, 62865187, 90508726, 128250760, 179101000, 246782250, 335859615, 451886526, 601568982 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. 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. 229). Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA From Colin Barker, Apr 22 2020: (Start) G.f.: (1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9. a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8. (End) Sum_{n>=0} 1/a(n) = 120*Pi^2 - 144*sqrt(5)*Pi*tan(sqrt(5)*Pi/2) - 790. - Amiram Eldar, May 31 2022 MAPLE a:=n->(1/720)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2+5*n+5): seq(a(n), n=0..30); MATHEMATICA Table[(n+1)(n+2)^2(n+3)^2(n+4)(n^2+5n+5)/720, {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 22, 190, 1015, 4018, 12936, 35784, 88110, 197835}, 30] (* Harvey P. Dale, Sep 27 2020 *) PROG (PARI) Vec((1 + 13*x + 28*x^2 + 13*x^3 + x^4) / (1 - x)^9 + O(x^30)) \\ Colin Barker, Apr 22 2020 CROSSREFS Sequence in context: A231749 A072040 A022682 * A200936 A110690 A020923 Adjacent sequences: A107956 A107957 A107958 * A107960 A107961 A107962 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 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 December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)