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 A038196 #15 Sep 12 2024 08:58:30
%S A038196 1,1,1,2,3,5,6,11,14,25,31,56,70,126,157,283,353,636,793,1429,1782,
%T A038196 3211,4004,7215,8997,16212,20216,36428,45425,81853,102069,183922,
%U A038196 229347,413269,515338,928607,1157954,2086561,2601899,4688460,5846414
%N A038196 3-wave sequence starting with 1, 1, 1.
%C A038196 The 3-wave sequence with initial values a, b, c is formed by the following construction:
%C A038196 a.......a+b+c............3a+5b+6c...
%C A038196 ..b...b+c...a+2b+2c..2a+4b+5c...
%C A038196 ....c..........a+2b+3c...
%D A038196 J. Kappraff, Beyond Measure, World Scientific, Inc. 2002, p. 497.
%H A038196 F. v. Lamoen, <a href="http://home.wxs.nl/~lamoen/wiskunde/wave.htm">Wave sequences</a>
%H A038196 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 0, 1, 0, -1).
%F A038196 a(n) = a(n-1) + a(n-2) if n is odd,
%F A038196 a(n) = a(n-1) + a(n-4) if n is even.
%F A038196 Also: a(n) = 2*a(n-2) + a(n-4) - a(n-6).
%F A038196 G.f.: (1 + x - x^2)/(1 - 2*x^2 - x^4 + x^6).
%o A038196 (PARI) a(n)=if(n>-1,polcoeff((1+x-x^2)/(1-2*x^2-x^4+x^6)+x*O(x^n),n),if(n<-3,polcoeff((1-x-x^2)/(1-x^2-2*x^4+x^6)+O(x^(-3-n)),-4-n),0))
%Y A038196 a(2n) forms A006356, a(2n+1) ("the middle row") forms A006054. Cf. A038197, A038201, A187070.
%K A038196 easy,nonn
%O A038196 0,4
%A A038196 _Floor van Lamoen_
%E A038196 Edited by _Floor van Lamoen_, Feb 05 2002