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 A105343 #39 Jan 23 2025 21:58:03
%S A105343 1,3,4,7,10,15,20,27,34,43,52,63,74,87,100,115,130,147,164,183,202,
%T A105343 223,244,267,290,315,340,367,394,423,452,483,514,547,580,615,650,687,
%U A105343 724,763,802,843,884,927,970,1015,1060,1107,1154,1203,1252,1303,1354,1407
%N A105343 Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1.
%C A105343 Floretion Algebra Multiplication Program, FAMP Code: 2jesforrokseq[E*F*sig(E)] with E = + .5i' + .5j' + .5'ki' + .5'kj', F the sum of all floretion basis vectors and "sig" the swap-operator. RokType: Y[15] = Y[15] + Math.signum(Y[15])*p (internal program code)
%C A105343 May be seen as the jesforrok-transform of the zero-sequence (A000004) with respect to the floretion given in the program code.
%C A105343 Identical to A267459(n+1) for n > 0. - _Guenther Schrack_, Jun 01 2018
%H A105343 Vincenzo Librandi, <a href="/A105343/b105343.txt">Table of n, a(n) for n = 0..10000</a>
%H A105343 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A105343 G.f.: (1 + x - 2*x^2 + x^3 + x^4)/((x+1)*(1-x)^3); a(n+2) - 2*a(n+1) + a(n) = (-1)^(n+1)*A084099(n).
%F A105343 a(n) = (1/4)*(2*n^2 + 9 - (-1)^n ), n>1. - _Ralf Stephan_, Jun 01 2007
%F A105343 Sum_{n>=0} 1/a(n) = 3/4 + tanh(sqrt(5)*Pi/2)*Pi/(2*sqrt(5)) + coth(Pi)*Pi/4. - _Amiram Eldar_, Sep 16 2022
%e A105343 G.f. = 1 + 3*x + 4*x^2 + 7*x^3 + 10*x^4 + 15*x^5 + 20*x^6 + 27*x^7 + ... - _Michael Somos_, Jun 26 2018
%t A105343 Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {3, 4, 7, 10}, 60]] (* _Jean-François Alcover_, Nov 13 2017 *)
%o A105343 (Magma) [1] cat [(2*n^2 + 9 - (-1)^n) div 4: n in [1..60]]; // _Vincenzo Librandi_, Oct 10 2011
%o A105343 (PARI) {a(n) = if( n<1, n==0, (2*n^2 + 10)\4)}; /* _Michael Somos_, Jun 26 2018 */
%Y A105343 Cf. A005893, A084099, A267459.
%K A105343 easy,nonn
%O A105343 0,2
%A A105343 _Creighton Dement_, Apr 30 2005