This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017847 #37 May 29 2025 16:39:18
%S A017847 1,0,0,0,0,0,1,1,0,0,0,0,1,2,1,0,0,0,1,3,3,1,0,0,1,4,6,4,1,0,1,5,10,
%T A017847 10,5,1,1,6,15,20,15,6,2,7,21,35,35,21,8,9,28,56,70,56,29,17,37,84,
%U A017847 126,126,85,46,54,121,210,252,211,131,100,175,331,462,463,342,231,275,506,793,925
%N A017847 Expansion of 1/(1 - x^6 - x^7).
%C A017847 Number of compositions of n into parts 6 and 7. - _Joerg Arndt_, Jun 27 2013
%H A017847 Harvey P. Dale, <a href="/A017847/b017847.txt">Table of n, a(n) for n = 0..1000</a>
%H A017847 Johann Cigler, <a href="https://arxiv.org/abs/2212.02118">Recurrences for certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials</a>, arXiv:2212.02118 [math.NT], 2022.
%H A017847 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1,1).
%F A017847 a(0)=1, a(1)=0,a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1; for n>6, a(n) = a(n-6)+a(n-7). - _Harvey P. Dale_, Dec 15 2012
%F A017847 a(n) = Sum_{k=0..floor(n/6)} binomial(k,n-6*k). - _Seiichi Manyama_, Oct 01 2024
%t A017847 CoefficientList[Series[1/(1-x^6-x^7), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {1, 0, 0, 0, 0, 0, 1}, 70] (* _Harvey P. Dale_, Dec 15 2012 *)
%t A017847 CoefficientList[Series[1 / (1 - Total[x^Range[6, 7]]),{x, 0, 70}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%o A017847 (Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7))); // _Vincenzo Librandi_, Jun 27 2013
%o A017847 (Magma) I:=[1,0,0,0,0,0,1]; [n le 7 select I[n] else Self(n-6)+Self(n-7): n in [1..70]]; // _Vincenzo Librandi_, Jun 27 2013
%Y A017847 Column k=6 of A306713.
%K A017847 nonn,easy
%O A017847 0,14
%A A017847 _N. J. A. Sloane_