A017881 Expansion of 1/(1 - x^9 - x^10 - x^11 - x^12 - x^13 - x^14).

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 3, 4, 6, 10, 15, 21, 25, 27, 27, 26, 25, 25, 30, 41, 59, 81, 104, 125, 141, 151, 155, 160, 174, 206, 261, 340, 440, 551, 661, 757, 836, 906, 987

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 9, 10, 11, 12, 13 and 14. - Ilya Gutkovskiy, May 27 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1,1,1,1,1,1).

Crossrefs

Cf. A017877, A017878, A017879, A017880, A017882, A017883, A017884, A017885, A017886.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!( (1-x)/(1-x-x^9+x^(15)) )); // G. C. Greubel, Sep 25 2024

Mathematica

CoefficientList[Series[1/(1-Total[x^Range[9,14]]),{x,0,60}],x] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,0,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,1,1,1,1,1}, 60] (* Harvey P. Dale, Feb 27 2012 *)

SageMath

def A017881_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^9+x^(15)) ).list()
A017881_list(80) # G. C. Greubel, Sep 25 2024

Formula

a(0)=1, a(1)=a(2)=a(3)=a(4)=a(5)=a(6)=a(7)=a(8)=0, a(9)=a(10)=a(11)=a(12)= a(13)=1, a(n) = a(n-9) + a(n-10) + a(n-11) + a(n-12) + a(n-13) + a(n-14). - Harvey P. Dale, Feb 27 2012