A017857 - OEIS

%I #32 Oct 01 2024 07:15:53

%S 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,

%T 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,

%U 28,9,10,36,84,126,126,84,37

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

%C Number of compositions of n into parts 7 and 8. - _Joerg Arndt_, Jun 28 2013

%H Vincenzo Librandi, <a href="/A017857/b017857.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1,1).

%F a(n) = a(n-7) + a(n-8) for n > 7. - _Vincenzo Librandi_, Jun 28 2013

%F a(n) = Sum_{k=0..floor(n/7)} binomial(k,n-7*k). - _Seiichi Manyama_, Oct 01 2024

%t CoefficientList[Series[1 / (1 - Total[x^Range[7, 8]]), {x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 28 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,1},80] (* _Harvey P. Dale_, Mar 19 2019 *)

%o (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-x^8))); /* or */ 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

%o (PARI) x='x+O('x^66); Vec(1/(1-x^7-x^8)) \\ _Altug Alkan_, Oct 07 2018

%Y Column k=7 of A306713.

%K nonn,easy

%O 0,16

%A _N. J. A. Sloane_