A097922 G.f.: (1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5)).

1, 1, 3, 4, 6, 9, 12, 16, 21, 26, 32, 39, 46, 54, 63, 72, 82, 93, 104, 116, 129, 142, 156, 171, 186, 202, 219, 236, 254, 273, 292, 312, 333, 354, 376, 399, 422, 446, 471, 496, 522, 549, 576, 604, 633, 662, 692, 723, 754, 786, 819, 852, 886, 921, 956, 992, 1029, 1066, 1104

Offset: 0

Author

N. J. A. Sloane, Sep 05 2004

Keywords

• nonn
• easy

References

• G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 188.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Programs

Magma

[1,1] cat [2 + Ceiling(n*(n-1)/3): n in [2..30]]; // G. C. Greubel, Dec 20 2017

Mathematica

CoefficientList[Series[(1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5)), {x,0,50}], x] (* or *) Join[{1,1}, LinearRecurrence[{2,-1,1,-2, 1}, {3, 4, 6, 9, 12}, 30]] (* or *) Join[{1,1}, Table[2 + Ceiling[n*(n-1)/3], {n,2,30}]] (* G. C. Greubel, Dec 20 2017 *)

PARI

x='x+O('x^30); Vec((1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5))) \\ G. C. Greubel, Dec 20 2017

PARI

for(n=0,30, print1(if(n==0, 1, if(n==1, 1, 2 + ceil(n*(n-1)/3))), ", ")) \\ G. C. Greubel, Dec 20 2017

Formula

a(n) = 2 + ceiling((n^2 - n)/3) for n >= 2. - Robert Israel, May 20 2014