

A029136


Expansion of 1/((1x^2)*(1x^3)*(1x^4)*(1x^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
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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), 8588, 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((n1)/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=j1) 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



