A017830 Expansion of 1/(1-x^4-x^5-x^6-x^7-x^8).

1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 17, 22, 29, 38, 51, 67, 89, 118, 157, 207, 274, 363, 482, 638, 845, 1119, 1483, 1964, 2602, 3447, 4567, 6049, 8013, 10615, 14063, 18629, 24678, 32691, 43307, 57369

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of compositions (ordered partitions) of n into parts 4, 5, 6, 7 and 8. - Ilya Gutkovskiy, May 25 2017

Links

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

Programs

Magma

I:=[1,0,0,0,1,1,1,1]; [n le 8 select I[n] else Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^4-x^5-x^6-x^7-x^8))); // Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1/(1 - Total[x^Range[4, 8]]), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Aug 05 2011 *)

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=1, a(7)=1; for n>7, a(n) = a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8). [Harvey P. Dale, Aug 05 2011]