|
| |
|
|
A108648
|
|
a(n) = (n+1)^2*(n+2)^3*(n+3)/24.
|
|
1
|
|
|
|
1, 18, 120, 500, 1575, 4116, 9408, 19440, 37125, 66550, 113256, 184548, 289835, 441000, 652800, 943296, 1334313, 1851930, 2527000, 3395700, 4500111, 5888828, 7617600, 9750000, 12358125, 15523326, 19336968, 23901220, 29329875, 35749200
(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. 230, no. 24).
|
|
|
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. 230, no. 24).
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
|
|
|
FORMULA
|
From Colin Barker, Apr 22 2020: (Start)
G.f.: (1 + 11*x + 15*x^2 + 3*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
a(n) = A000217(n+1) * A002415(n+2). - J. M. Bergot, May 21 2022
From Amiram Eldar, May 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 24*zeta(3) + 6*Pi^2 - 87.
Sum_{n>=0} (-1)^n/a(n) = 99 - Pi^2 - 96*log(2) - 18*zeta(3). (End)
|
|
|
MAPLE
|
a:=(n+1)^2*(n+2)^3*(n+3)/24: seq(a(n), n=0..36);
|
|
|
PROG
|
(PARI) Vec((1 + 11*x + 15*x^2 + 3*x^3) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Apr 22 2020
|
|
|
CROSSREFS
|
Sequence in context: A044350 A044731 A190705 * A264360 A223046 A037064
Adjacent sequences: A108645 A108646 A108647 * A108649 A108650 A108651
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Emeric Deutsch, Jun 13 2005
|
|
|
STATUS
|
approved
|
| |
|
|
