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 A111954 #30 Sep 07 2024 01:06:50
%S A111954 1,0,3,4,13,28,71,168,409,984,2379,5740,13861,33460,80783,195024,
%T A111954 470833,1136688,2744211,6625108,15994429,38613964,93222359,225058680,
%U A111954 543339721,1311738120,3166815963,7645370044,18457556053,44560482148,107578520351
%N A111954 a(n) = A000129(n) + (-1)^n.
%C A111954 a(n) + a(n+1) = A001333(n+1). Inverse binomial transform of A007070 (with prepended 1). Inverse invert transform of A077995.
%C A111954 Floretion Algebra Multiplication Program, FAMP Code: -4ibasejseq[J*D] with J = - .25'i + .25'j + .5'k - .25i' + .25j' + .5k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and D = + .5'i - .25'j + .25'k + .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
%H A111954 Harvey P. Dale, <a href="/A111954/b111954.txt">Table of n, a(n) for n = 0..1000</a>
%H A111954 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,1).
%F A111954 a(n) = a(n-1) + 3*a(n-2) + a(n-3), n >= 3.
%F A111954 G.f.: (x-1)/((x+1)*(x^2+2*x-1)).
%F A111954 a(n) = (sqrt(2)/4)*((1 + sqrt(2))^n - (1 - sqrt(2))^n) + (-1)^n.
%F A111954 E.g.f.: cosh(x) - sinh(x) + exp(x)*sinh(sqrt(2)*x)/sqrt(2). - _Stefano Spezia_, May 26 2024
%t A111954 LinearRecurrence[{1,3,1},{1,0,3},40] (* _Harvey P. Dale_, Nov 24 2014 *)
%Y A111954 Cf. A000129, A001333, A111955, A111956, A007070, A077995.
%K A111954 easy,nonn
%O A111954 0,3
%A A111954 _Creighton Dement_, Aug 23 2005