A038167 G.f.: x*(1+3*x+x^2)/((1-x^2)^2*(1-x^5)).

0, 1, 3, 3, 6, 5, 10, 10, 15, 15, 20, 21, 28, 28, 36, 35, 45, 45, 55, 55, 65, 66, 78, 78, 91, 90, 105, 105, 120, 120, 135, 136, 153, 153, 171, 170, 190, 190, 210, 210, 230, 231, 253, 253, 276, 275, 300, 300, 325, 325, 350, 351, 378, 378, 406, 405

Offset

0,3

References

S. J. Cyvin et al., Polygonal systems including the corannulene and coronene homologs: novel applications of Pólya's theorem, Z. Naturforsch., 52a (1997), 867-873.

Links

Table of n, a(n) for n=0..55.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1,1,0,-2,0,1).

Formula

a(n)=5n/8+39/80+n^2/8+(-1)^n*(n/8+5/16)-(4*A010891(n)+3*A010891(n-1)+2*A010891(n-2)+A010891(n-3))/5. - R. J. Mathar, Jun 17 2009

Maple

A010891 := proc(n) op((n mod 5)+1, [1, -1, 0, 0, 0]) ; end:
A038167 := proc(n) 5*n/8+39/80+n^2/8+(-1)^n*(n/8+5/16) -(4*A010891(n)+3*A010891(n-1)+2*A010891(n-2)+A010891(n-3))/5 ; end:
seq(A038167(n), n=0..30) ; # R. J. Mathar, Jun 17 2009

Mathematica

CoefficientList[Series[x (1+3x+x^2)/((1-x^2)^2(1-x^5)), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 2, 0, -1, 1, 0, -2, 0, 1}, {0, 1, 3, 3, 6, 5, 10, 10, 15}, 60] (* Harvey P. Dale, Aug 03 2017 *)

Crossrefs

Sequence in context: A080512 A225441 A102245 * A307967 A131077 A357897

Adjacent sequences: A038164 A038165 A038166 * A038168 A038169 A038170

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved