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A114243 a(n) = (n+1)(n+2)^2*(n+3)(n+4)(3n+5)/240. 0
1, 12, 66, 245, 714, 1764, 3864, 7722, 14355, 25168, 42042, 67431, 104468, 157080, 230112, 329460, 462213, 636804, 863170, 1152921, 1519518, 1978460, 2547480, 3246750, 4099095, 5130216, 6368922, 7847371, 9601320, 11670384, 14098304, 16933224, 20227977 (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 (pp. 167-169, Table 10.5/II/3).

LINKS

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: (1 + 5*x + 3*x^2)/(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). - Wesley Ivan Hurt, May 03 2015

MAPLE

a:=n->(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240: seq(a(n), n=0..35);

MATHEMATICA

CoefficientList[Series[(1+5x+3x^2)/(1-x)^7, {x, 0, 40}], x]  (* Harvey P. Dale, Feb 19 2011 *)

Table[(n + 1) (n + 2)^2 (n + 3) (n + 4) (3 n + 5) / 240, {n, 0, 50}] (* Vincenzo Librandi, May 03 2015 *)

PROG

(MAGMA) [(n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240 : n in [0..50]]; // Wesley Ivan Hurt, May 03 2015

CROSSREFS

Sequence in context: A007249 A112142 A271870 * A000972 A180392 A161805

Adjacent sequences:  A114240 A114241 A114242 * A114244 A114245 A114246

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 18 2005

STATUS

approved

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Last modified April 21 04:56 EDT 2019. Contains 322310 sequences. (Running on oeis4.)