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 A007904 #43 Jan 22 2024 14:53:28
%S A007904 1,5,17,41,83,147,239,363,525,729,981,1285,1647,2071,2563,3127,3769,
%T A007904 4493,5305,6209,7211,8315,9527,10851,12293,13857,15549,17373,19335,
%U A007904 21439,23691,26095,28657,31381,34273,37337,40579,44003,47615,51419,55421,59625,64037
%N A007904 Crystal ball sequence for diamond.
%C A007904 Binomial transform of [1, 4, 8, 4, 2, -4, 8, -16, 32, -64, 128, ...]. - _Gary W. Adamson_, Feb 07 2010
%H A007904 T. D. Noe, <a href="/A007904/b007904.txt">Table of n, a(n) for n = 0..1000</a>
%H A007904 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A007904 <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%H A007904 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -2, 3, -1).
%F A007904 G.f.: -(x^4 + 2*x^3 + 4*x^2 + 2*x + 1)/((x-1)^2*(x^2-1)*(1-x)).
%F A007904 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5). - _Wesley Ivan Hurt_, Jan 20 2024
%p A007904 gf:= -(x^4+2*x^3+4*x^2+2*x+1)/((x-1)^2*(x^2-1)*(1-x)):
%p A007904 seq(coeff(series(gf,x,n+1),x,n), n=0..50);
%t A007904 b[0]=1; b[1]=4; b[2]=8; b[3]=4; b[n_] := (-1)^n*2^(n-3); a[n_] := Sum[Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Aug 08 2012, after _Gary W. Adamson_ *)
%t A007904 LinearRecurrence[{3,-2,-2,3,-1},{1,5,17,41,83},80] (* _Harvey P. Dale_, Jan 22 2024 *)
%Y A007904 Partial sums of A008253.
%K A007904 nonn,nice
%O A007904 0,2
%A A007904 _N. J. A. Sloane_