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A029136 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Wesley Ivan Hurt, Jul 08 2014

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)