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 A237716 #40 Nov 07 2024 08:30:24
%S A237716 1,1,1,1,1,1,1,3,3,5,5,7,7,9,13,15,23,25,37,39,55,65,85,111,135,185,
%T A237716 213,295,343,465,565,735,935,1161,1525,1847,2455,2977,3925,4847,6247,
%U A237716 7897,9941,12807,15895,20657,25589,33151,41383,53033,66997
%N A237716 7-distance Pell sequence.
%H A237716 G. C. Greubel, <a href="/A237716/b237716.txt">Table of n, a(n) for n = 0..1000</a>
%H A237716 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,2).
%F A237716 a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1; a(n) = 2*a(n-7) + a(n-2) for n>=7.
%F A237716 G.f.: (1 + x)/(1 - x^2 - 2*x^7).
%F A237716 a(2*n) = Sum_{j=0..n/7} binomial(n-5*j, 2*j)*2^(2*j) + Sum_{j=0..(n-4)/7} binomial(n-3-5*j, 2*j+1)*2^(2*j+1).
%F A237716 a(2*n+1) = Sum_{j=0..n/7} binomial(n-5*j, 2*j)*2^(2*j) + Sum_{j=0..(n-3)/7} binomial(n-2-5*j, 2*j+1)*2^(2*j+1).
%e A237716 a(7)=2a(0)+a(5)=3; a(8)=2a(1)+a(6)=3; a(9)=2a(2)+a(7)=5.
%t A237716 For[j = 0, j < 7, j++, a[j] = 1]
%t A237716 For[j = 7, j < 51, j++, a[j] = 2 a[j - 7] + a[j - 2]]
%t A237716 Table[a[j], {j, 0, 50}]
%t A237716 CoefficientList[Series[(1 + x)/(1 - x^2 - 2 x^7), {x,0,50}], x] (* _G. C. Greubel_, May 01 2017 *)
%o A237716 (PARI) Vec((1+x)/(1-x^2-2*x^7)+O(x^99)) \\ _Charles R Greathouse IV_, Mar 06 2014
%Y A237716 Cf. A000129, A122522, A159284, A237714.
%K A237716 nonn,easy
%O A237716 0,8
%A A237716 _Sergio Falcon_, Feb 12 2014