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A107966
a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(5n^2 + 23n + 30)/8640.
1
1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421, 3955952, 7966322, 15249780, 27941200, 49273344, 84012300, 139021461, 223980645, 352290400, 542195192, 818163038, 1212563220, 1767688000, 2538168750, 3593841615
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
LINKS
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 (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(0)=1, a(1)=29, a(2)=320, a(3)=2100, a(4)=9898, a(5)=37044, a(6)=116928, a(7)=323730, a(8)=807675, a(9)=1851421, a(n)=10*a(n-1)- 45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)- 45*a(n-8)+ 10*a(n-9)-a(n-10). - Harvey P. Dale, Apr 18 2016
G.f.: (1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10. - Colin Barker, Apr 22 2020
MAPLE
a:=n->(1/8640)*(n+1)*(n+2)^3*(n+3)^2*(n+4)*(5*n^2+23*n+30): seq(a(n), n=0..26);
MATHEMATICA
Table[(n+1)(n+2)^3(n+3)^2(n+4)(5n^2+23n+30)/8640, {n, 0, 30}] (* or *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 29, 320, 2100, 9898, 37044, 116928, 323730, 807675, 1851421}, 30] (* Harvey P. Dale, Apr 18 2016 *)
PROG
(PARI) Vec((1 + 19*x + 75*x^2 + 85*x^3 + 28*x^4 + 2*x^5) / (1 - x)^10 + O(x^30)) \\ Colin Barker, Apr 22 2020
CROSSREFS
Sequence in context: A165616 A142380 A042632 * A057131 A160442 A125417
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved