A017857 Expansion of 1/(1 - x^7 - x^8).

1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 1, 5, 10, 10, 5, 1, 0, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 2, 8, 28, 56, 70, 56, 28, 9, 10, 36, 84, 126, 126, 84, 37

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 7 and 8. - Joerg Arndt, Jun 28 2013

Links

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

Crossrefs

Column k=7 of A306713.

Programs

Magma

m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8))); // Vincenzo Librandi, Jun 28 2013

Magma

I:=[1,0,0,0,0,0,0,1]; [n le 8 select I[n] else Self(n-7)+Self(n-8): n in [1..70]]; // Vincenzo Librandi, Jun 28 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[7, 8]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,1},80] (* Harvey P. Dale, Mar 19 2019 *)

PARI

x='x+O('x^66); Vec(1/(1-x^7-x^8)) \\ Altug Alkan, Oct 07 2018

Formula

a(n) = a(n-7) + a(n-8) for n > 7. - Vincenzo Librandi, Jun 28 2013

a(n) = Sum_{k=0..floor(n/7)} binomial(k,n-7*k). - Seiichi Manyama, Oct 01 2024