A017893 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 6, 7, 9, 12, 16, 21, 28, 36, 42, 46, 49, 52, 56, 62, 71, 84, 105, 135, 171, 210, 250, 290, 330, 371, 414, 462, 525, 614, 736, 894, 1088, 1316, 1575, 1862, 2171, 2498, 2852, 3256, 3742, 4346, 5104, 6049, 7210, 8610

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, 16 and 17. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1).

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-x^17))); // Vincenzo Librandi, Jul 01 2013

Maple

a:= n-> (Matrix(17, (i, j)-> if (i=j-1) or (j=1 and i in [$10..17]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # Alois P. Heinz, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 17]]), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1},80] (* Harvey P. Dale, Dec 02 2024 *)

SageMath

def A017893_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^18) ).list()
A017893_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(n-17), n>16. - Vincenzo Librandi, Jul 01 2013