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A107963 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360. 5

%I

%S 1,13,73,273,798,1974,4326,8646,16071,28171,47047,75439,116844,175644,

%T 257244,368220,516477,711417,964117,1287517,1696618,2208690,2843490,

%U 3623490,4574115,5723991,7105203,8753563,10708888,13015288,15721464

%N a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360.

%C Kekulé numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).

%H Vincenzo Librandi, <a href="/A107963/b107963.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1)

%F G.f.: ( -1-6*x-3*x^2 ) / (x-1)^7 . - _R. J. Mathar_, Feb 16 2011

%F a(n) = Sum_{i=0..n+1} A000217(i)*A000292(i) with a(-1)=0. - _Bruno Berselli_, Jul 20 2015

%p a:=n->(1/360)*(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15): seq(a(n),n=0..36);

%t LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 13, 73, 273, 798, 1974, 4326}, 40] (* _Vincenzo Librandi_, Apr 23 2017 *)

%o (PARI) a(n)=(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15)/360 \\ _Charles R Greathouse IV_, Oct 16 2015

%o (MAGMA) [(n+1)*(n+2)*(n+3)*(n+4)*(5*n^2+19*n+15)/360: n in [0..30]]; // _Vincenzo Librandi_, Apr 23 2017

%Y Equals third right hand column of A161739 (RSEG2 triangle). - _Johannes W. Meijer_, Jun 18 2009

%Y Cf. A000217, A000292.

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Jun 12 2005

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Last modified July 11 08:50 EDT 2020. Contains 335626 sequences. (Running on oeis4.)