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A121127 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition). 1
1, 7, 73, 747, 7218, 65583, 567540, 4725540, 38145600, 300244320, 2314123992, 17522693064, 130682767824, 961866429552, 6998356983168, 50401223526528, 359691525797760, 2546051729270400, 17889363288835200, 124855271993773440, 866077921088785152, 5974010552957001984, 40994676513378284544 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

COMMENTS

For r >= 4, a(r) is the total number of isomers of unbranched alpha-4-catapolynonagons with q = 9 and alpha = 4. Here alpha = 4 is the number of tetragons and r - alpha = r - 4 is the number of q-gons (9-gons) in the alpha-4-catafusene. - Petros Hadjicostas, Jul 31 2019

LINKS

Table of n, a(n) for n=4..26.

J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, Isomer enumeration of polygonal systems representing polycyclic conjugated hydrocarbons: unbranched catacondensed systems with tetragons and q-gons, J. Molec. Struct. (Theochem), 364 (1996), 1-13; see Table 12 with q = 9 and alpha = 4.

Index entries for linear recurrences with constant coefficients, signature (30,-342,1620,-108,-27864,77976,86832,-622080,373248,1399680,-1679616).

FORMULA

G.f. x^4 +7*x^5 +73*x^6 -9*x^7*(-83 +1688*x -11613*x^2 +15726*x^3 +164862*x^4 -647508*x^5 -283716*x^6 +4642272*x^7 -3888000*x^8 -10101024*x^9 +13576896*x^10) / ( (6*x^2-1)^3*(6*x-1)^5 ). - R. J. Mathar, Aug 01 2019

MAPLE

# Using the "master formula" in Exhibit 4 (p. 13) with q = 9 and alpha = 4:

a := proc(r) 1/4*6^(r - 6)*(36*binomial(r - 2, 2) + 12*binomial(r - 2, 3) + binomial(r - 2, 4)) + 1/4*binomial(2, r - 4) + (1 - 1/2*(-1)^r)*(6*floor(1/2*r) - 6 + binomial(floor(1/2*r) - 1, 2))*6^(floor(1/2*r) - 3); end;

seq(a(r), r = 4 .. 30); # Petros Hadjicostas, Jul 31 2019

CROSSREFS

Sequence in context: A155614 A113033 A093675 * A071060 A092444 A099141

Adjacent sequences:  A121124 A121125 A121126 * A121128 A121129 A121130

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 13 2006

EXTENSIONS

More terms from Petros Hadjicostas, Jul 31 2019

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)