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 A167051 #10 Jun 02 2025 02:09:56
%S A167051 1,2,4,7,8,10,25,26,28,79,80,82,241,242,244,727,728,730,2185,2186,
%T A167051 2188,6559,6560,6562,19681,19682,19684,59047,59048,59050,177145,
%U A167051 177146,177148,531439,531440,531442,1594321,1594322,1594324,4782967,4782968,4782970,14348905
%N A167051 Start at 1, then add the first term (which is one here) plus 1 for the second term; then add the second term plus 2 for the third term; then add the third term to the sum of the first and second term; this gives the fourth term. Restart the sequence by adding 1 to the fourth term, etc. (From a sixth grade math extra credit assignment).
%H A167051 Andrew Howroyd, <a href="/A167051/b167051.txt">Table of n, a(n) for n = 1..1000</a>
%F A167051 a(n) = a(n-1) + 1 for n mod 3 == 2;
%F A167051 a(n) = a(n-1) + 2 for n mod 3 == 0;
%F A167051 a(n) = a(n-1) + a(n-2) + a(n-3) for n mod 3 == 1 and n > 1.
%F A167051 G.f.: x*(1 + 2*x + 4*x^2 + 3*x^3 - 6*x^5)/((1 - x)*(1 + x + x^2)*(1 - 3*x^3)). - _Andrew Howroyd_, Apr 13 2021
%o A167051 (PARI) seq(n)={my(a=vector(n)); a[1]=1; for(n=2, #a, my(t=n%3); a[n]=a[n-1]+if(t==2, 1, if(t==0, 2, a[n-2]+a[n-3]))); a} \\ _Andrew Howroyd_, Apr 13 2021
%o A167051 (PARI) Vec((1 + 2*x + 4*x^2 + 3*x^3 - 6*x^5)/((1 - x)*(1 + x + x^2)*(1 - 3*x^3)) + O(x^40)) \\ _Andrew Howroyd_, Apr 13 2021
%K A167051 nonn
%O A167051 1,2
%A A167051 Chris Rice (cwrice(AT)research.att.com), Oct 27 2009