The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108678 a(n) = (n+1)^2*(n+2)*(2*n+3)/6. 5
 1, 10, 42, 120, 275, 546, 980, 1632, 2565, 3850, 5566, 7800, 10647, 14210, 18600, 23936, 30345, 37962, 46930, 57400, 69531, 83490, 99452, 117600, 138125, 161226, 187110, 215992, 248095, 283650, 322896, 366080, 413457, 465290, 521850, 583416, 650275, 722722 (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. 232, # 44). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: (1 + 5*x + 2*x^2)/(1-x)^5. a(n) = A098077(n+1)/2. - Alexander Adamchuk, Apr 12 2006 From Amiram Eldar, May 31 2022: (Start) Sum_{n>=0} 1/a(n) = Pi^2 + 48*log(2) - 42. Sum_{n>=0} (-1)^n/a(n) = Pi^2/2 - 12*Pi - 12*log(2) + 42. (End) From G. C. Greubel, Apr 09 2023: (Start) a(n) = (1/3)*binomial(n+2, 2)*binomial(2*n+3, 2). a(n) = (1/3)*A000217(n+1)*A014105(n+1) a(n) = (1/8)*A100431(n). E.g.f.: (1/6)*(6 + 54*x + 69*x^2 + 23*x^3 + 2*x^4)*exp(x). (End) a(n) = (n+1)*A000330(n+1). - Olivier Gérard, Jan 13 2024 MAPLE a:=n->(n+1)^2*(n+2)*(2*n+3)/6: seq(a(n), n=0..42); a:=n->sum(n*j^2, j=1..n): seq(a(n), n=1..36); # Zerinvary Lajos, Apr 29 2007 MATHEMATICA Table[(n+1)^2*(n+2)(2n+3)/6, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *) PROG (Magma) [(n+1)^2*(n+2)*(2*n+3)/6: n in [0..60]]; // G. C. Greubel, Apr 09 2023 (SageMath) [(n+1)^2*(n+2)*(2*n+3)/6 for n in range(61)] # G. C. Greubel, Apr 09 2023 CROSSREFS Cf. A000217, A014105, A098077, A100431. Sequence in context: A372666 A328536 A163815 * A226988 A358249 A027171 Adjacent sequences: A108675 A108676 A108677 * A108679 A108680 A108681 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 17 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 May 23 05:47 EDT 2024. Contains 372758 sequences. (Running on oeis4.)