A017896 Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19-x^20).

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 18, 22, 27, 33, 40, 48, 57, 68, 79, 92, 107, 125, 147, 174, 207, 247, 295, 353, 420, 499, 591, 698, 823, 970, 1144, 1351, 1598, 1894, 2246, 2666, 3165, 3756, 4454, 5277, 6247, 7391, 8742, 10341, 12234

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, 19 and 20. - 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 (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1).

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-x^20))); // Vincenzo Librandi, Jul 01 2013

Maple

a:= n-> (Matrix(20, (i, j)-> if (i=j-1) or (j=1 and i in [$10..20]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..80);  # Alois P. Heinz, Aug 04 2008

Mathematica

CoefficientList[Series[1/(1 -Total[x^Range[10, 20]]), {x,0,80}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0, 0,0,1,1,1,1,1,1,1,1,1,1}, 81] (* Harvey P. Dale, Oct 21 2016 *)

SageMath

def A017896_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-x)/(1-x-x^10+x^21) ).list()
A017896_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) +a(n-20), for n>19. - Vincenzo Librandi, Jul 01 2013