A029136 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)).

1, 0, 1, 1, 2, 1, 4, 2, 5, 4, 7, 5, 11, 7, 13, 11, 17, 13, 23, 17, 27, 23, 33, 27, 42, 33, 48, 42, 57, 48, 69, 57, 78, 69, 90, 78, 106, 90, 118, 106, 134, 118, 154, 134, 170, 154, 190, 170, 215, 190, 235, 215, 260, 235, 290, 260, 315, 290, 345, 315, 381, 345

Offset

0,5

Comments

Number of nonisomorphic hollow hexagons with n hexagons for n >= 8 (a class of primitive coronoids).

Number of partitions of n into parts 2, 3, 4, and 6. - Joerg Arndt, Jul 09 2014

References

B. N. Cyvin et al., Enumeration of conjugated hydrocarbons..., Structural Chem., 6 (1995), 85-88, equations (1)-(5) and (24).

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Tricia Muldoon Brown, Lattice path coronoids, Open J. Disc. Appl. Math. (2023) Vol. 6, No. 3, 1-21.

Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,-1,0,-1,-1,0,-1,1,1,1,0,-1).

Formula

a(n) = floor((2*n^3 + 45*n^2 + (273 + 96*(floor(n/3) - floor((n-1)/3)))*n + 1284 + 3*(3*n^2 + 45*n + 148)*(-1)^n)/1728). - Tani Akinari, Jul 08 2014

a(i+15) - a(i+13) - a(i+12) - a(i+11) + a(i+10) + a(i+8) + a(i+7) + a(i+5) - a(i+4) - a(i+3) - a(i+2) + a(i) = 0. - Robert Israel, Jul 08 2014

Maple

M := Matrix(15, (i, j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 4, 11, 12, 13])) then 1 elif j=1 and member(i, [5, 7, 8, 10, 15]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..53); # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1 - x^2)*(1 - x^3)*(1 - x^4)*(1 - x^6)), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jul 08 2014 *)

Prog

(PARI) a(n)=(2*n^3+45*n^2+(273+96*(n%3<1))*n+1284+3*(3*n^2+45*n+148)*(-1)^n)\1728 \\ Tani Akinari, Jul 08 2014

Crossrefs

Sequence in context: A106044 A124896 A008742 * A001479 A128861 A161307

Adjacent sequences: A029133 A029134 A029135 * A029137 A029138 A029139

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, Jul 08 2014

Status

approved