A017876 Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 10, 13, 17, 20, 24, 29, 35, 42, 51, 63, 79, 97, 118, 143, 174, 211, 256, 312, 383, 470, 575, 701, 855, 1042, 1269, 1546, 1887, 2306, 2818, 3440, 4198, 5122, 6248, 7620, 9296, 11346, 13852, 16909

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts p where 8 <= p <= 18. - Joerg Arndt, Jun 29 2013

Links

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

Programs

Magma

m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18))); // Vincenzo Librandi, Jun 29 2013

Magma

I:=[1,0,0,0,0,0,0,0,1,1,1,1,1, 1,1,1,2,3]; [n le 18 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17)+Self(n-18): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013

Mathematica

CoefficientList[Series[1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16 -x^17-x^18), {x, 0, 80}], x] (* Stefan Steinerberger, Apr 10 2006 *)
CoefficientList[Series[1 / (1 - Total[x^Range[8, 18]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1},{1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,3},70] (* Harvey P. Dale, Jan 04 2017 *)

PARI

my(x='x+O('x^70)); Vec((1-x)/(1-x-x^8+x^19)) \\ G. C. Greubel, Mar 19 2019

Sage

((1-x)/(1-x-x^8+x^19)).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Mar 19 2019

Formula

a(n) = a(n-8) +a(n-9) +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) for n>17. - Vincenzo Librandi, Jun 29 2013

G.f.: (1 - x)/(1 - x - x^8 + x^19). - G. C. Greubel, Mar 19 2019

Extensions

More terms from Stefan Steinerberger, Apr 10 2006