A017892 Expansion of 1/(1 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 4, 5, 7, 10, 15, 21, 28, 33, 36, 37, 37, 37, 38, 41, 50, 66, 90, 119, 150, 180, 207, 229, 246, 259, 276, 306, 359, 441, 554, 696, 862, 1041, 1221, 1390, 1547, 1703, 1882, 2116, 2441, 2891, 3494, 4259, 5174, 6205

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15 and 16. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1).

Crossrefs

Cf. A017887.

Programs

Magma

R:=PowerSeriesRing(Integers(), 80);
Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16))); // Vincenzo Librandi, Jul 01 2013

Maple

a[0]:= 1:
for i from 1 to 9 do a[i]:= 0 od:
for i from 10 to 15 do a[i]:= 1 od:
for i from 16 to 1000 do a[i]:= add(a[j],j=i-16 .. i-10) od:
seq(a[i],i=0..1000); # Robert Israel, Aug 15 2014

Mathematica

(* From Harvey P. Dale, Mar 04 2013: (Start) *)
CoefficientList[Series[1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16),{x,0,80}],x]
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1}, {1,0,0,0,0,0,0,0,0,0,1, 1,1,1,1,1},70] (* End *)
CoefficientList[Series[1/(1 - Total[x^Range[10, 16]]), {x,0,80}], x] (* Vincenzo Librandi, Jul 01 2013 *)

PARI

my(x='x+O('x^80)); Vec(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16)) \\ Altug Alkan, Oct 04 2018

SageMath

def A017892_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^17) ).list()
A017892_list(80) # G. C. Greubel, Nov 06 2024

Formula

a(n) = a(n-10) + a(n-11) + a(n-12) + a(n-13) + a(n-14) + a(n-15) + a(n-16); a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=1, a(11)=1, a(12)=1, a(13)=1, a(14)=1, a(15)=1. - Harvey P. Dale, Mar 04 2013