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

Author

N. J. A. Sloane, Aug 13 2006

Keywords

• nonn
• easy

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

• 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).

Programs

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

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 [phone]*x^10) / ( (6*x^2-1)^3*(6*x-1)^5 ). - R. J. Mathar, Aug 01 2019

Extensions

More terms from Petros Hadjicostas, Jul 31 2019