A008813 Expansion of (1+x^6)/((1-x)^2*(1-x^6)).

1, 2, 3, 4, 5, 6, 9, 12, 15, 18, 21, 24, 29, 34, 39, 44, 49, 54, 61, 68, 75, 82, 89, 96, 105, 114, 123, 132, 141, 150, 161, 172, 183, 194, 205, 216, 229, 242, 255, 268, 281, 294, 309, 324, 339, 354, 369, 384, 401, 418, 435, 452, 469, 486, 505, 524, 543, 562

Offset

0,2

Comments

Number of 0..n arrays of 7 elements with zero second differences. - R. H. Hardin, Nov 16 2011

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1+x^6)/((1-x)^2*(1-x^6)).

a(n) = 2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8). - R. H. Hardin, Nov 16 2011

Maple

seq(coeff(series((1+x^6)/((1-x)^2*(1-x^6)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019

Mathematica

CoefficientList[Series[(1+x^6)/(1-x)^2/(1-x^6), {x, 0, 70}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 9, 12}, 70] (* Harvey P. Dale, Oct 13 2012 *)

Prog

(PARI) Vec((1+x^6)/((1-x)^2*(1-x^6)) +O(x^70)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x)^2*(1-x^6)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008813_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^6)/((1-x)^2*(1-x^6))).list()
A008813_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 2, 3, 4, 5, 6, 9, 12];; for n in [9..70] do a[n]:=2*a[n-1]-a[n-2] +a[n-6]-2*a[n-7]+a[n-8]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), A008810 (m=3), A008811 (m=4), A008812 (m=5), this sequence (m=6), A008814 (m=7), A008815 (m=8), A008816 (m=9), A008817 (m=10).

Sequence in context: A091179 A036027 A036032 * A133463 A187550 A307818

Adjacent sequences: A008810 A008811 A008812 * A008814 A008815 A008816

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 12 2019

Status

approved