A017895 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 64, 73, 83, 95, 110, 129, 153, 183, 220, 265, 319, 381, 451, 530, 620, 724, 846, 991, 1165, 1375, 1630, 1938, 2306, 2741, 3251, 3846, 4539, 5347, 6292, 7402, 8713, 10270

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, 17, 18 and 19. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).

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-x^18-x^19))); // Vincenzo Librandi, Jul 01 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[10, 19]]), {x, 0, 70}], x] (* Vincenzo Librandi Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1},80] (* Harvey P. Dale, Apr 07 2025 *)

SageMath

def A017895_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^20) ).list()
A017895_list(81) # G. C. Greubel, Nov 08 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) +a(n-18) +a(n-19) for n>18. - Vincenzo Librandi, Jul 01 2013