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 A100215 #37 Mar 30 2024 13:24:39
%S A100215 4,9,14,18,24,44,104,248,544,1104,2144,4128,8064,16064,32384,65408,
%T A100215 131584,263424,525824,1049088,2095104,4189184,8382464,16775168,
%U A100215 33562624,67129344,134242304,268443648,536838144
%N A100215 Expansion of (4 - 7*x + 2*x^2)/((1-2*x)*(1 - 2*x + 2*x^2)).
%C A100215 a(n) = (-1)^n*A009116(n+3) + A100216(n) + A038503(n+1), where A009116, A100216 and A038503 can be generated by the operators jes, les and tes of the Floretion algebra, which is a product factor space Q x Q /{(1,1), (-1,-1)}.
%C A100215 Binomial transform of the sequence 4,5,0,-1 (repeated with period length 4). - _R. J. Mathar_, Apr 18 2009
%H A100215 Vincenzo Librandi, <a href="/A100215/b100215.txt">Table of n, a(n) for n = 0..1000</a>
%H A100215 Creighton Dement, <a href="https://web.archive.org/web/20201230160447/http://fumba.eu/sitelayout/Floretion.php">Floretion Online Multiplier</a>.
%H A100215 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4).
%F A100215 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3).
%F A100215 a(n) = (-1)^n*A009116(n+3) + A100216(n) + A038503(n+1).
%F A100215 a(n) = vesseq(.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e), where ves sums over all floretion basis vector coefficients.
%F A100215 a(n) = 2^(n+1) + 2*A099087(n) + A099087(n-1). - _R. J. Mathar_, Apr 18 2009
%e A100215 a(2) = 14 because (.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e)^3 = 1'j + 1'k + 1j' + 1k' + 3'ii' + 2'jj' + 2'kk' + 1'jk' + 1'kj' + 1e and the sum of these coefficients is 1 + 1 + 1 + 1 + 3 + 2 + 2 + 1 + 1 + 1 = 14 (see comment).
%t A100215 LinearRecurrence[{4,-6,4},{4,9,14},40] (* _Vincenzo Librandi_, Jun 25 2012 *)
%o A100215 (Magma) I:=[4, 9, 14]; [n le 3 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3): n in [1..35]]; // _Vincenzo Librandi_, Jun 25 2012
%o A100215 (SageMath)
%o A100215 A099087=BinaryRecurrenceSequence(2,-2,1,2)
%o A100215 def A100215(n): return 2^(n+1) + 2*A099087(n) + A099087(n-1)
%o A100215 [A100215(n) for n in range(41)] # _G. C. Greubel_, Mar 29 2024
%Y A100215 Cf. A009116, A038503, A099087, A100213, A100214, A100216.
%K A100215 nonn,easy
%O A100215 0,1
%A A100215 _Creighton Dement_, Nov 11 2004
%E A100215 Definition replaced with the more precise g.f. by _R. J. Mathar_, Nov 17 2010