A129026 - OEIS

%I #20 Sep 08 2022 08:45:30

%S 0,27,108,282,600,1125,1932,3108,4752,6975,9900,13662,18408,24297,

%T 31500,40200,50592,62883,77292,94050,113400,135597,160908,189612,

%U 222000,258375,299052,344358,394632,450225,511500,578832,652608,733227,821100,916650

%N a(n) = (1/2)*(n^4 + 11*n^3 + 53*n^2 + 97*n + 54).

%D Gordon G. Cash and Jerry Ray Dias, Computation, Properties and Resonance Topology of Benzenoid Monoradicals and Polyradicals and the Eigenvectors Belonging to Their Zero Eigenvalues, J. Math. Chem., 30 (2001), 429-444. [See Fig. 2.]

%H Vincenzo Librandi, <a href="/A129026/b129026.txt">Table of n, a(n) for n = -1..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (n+1)*(n+2)*(n^2 + 8*n + 27)/2 = A000217(n+1)*A189836(n+4). - _Bruno Berselli_, Sep 25 2011

%F G.f.: -3*(4*x^2 - 9*x + 9) / (x-1)^5. - _Colin Barker_, Jul 27 2013

%t Table[(n^4+11n^3+53n^2+97n+54)/2,{n,-1,40}] (* _Harvey P. Dale_, Sep 24 2011 *)

%o (Magma) [(1/2)*(n^4+11*n^3+53*n^2+97*n+54): n in [-1..40]]; // _Vincenzo Librandi_, Sep 25 2011

%K nonn,easy

%O -1,2

%A _N. J. A. Sloane_, May 10 2007