A121127 Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition).

1, 7, 73, 747, 7218, 65583, 567540, 4725540, 38145600, 300244320, 2314123992, 17522693064, 130682767824, 961866429552, 6998356983168, 50401223526528, 359691525797760, 2546051729270400, 17889363288835200, 124855271993773440, 866077921088785152, 5974010552957001984, 40994676513378284544

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