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 A016290 #61 Mar 26 2025 15:23:02
%S A016290 1,14,140,1240,10416,85344,690880,5559680,44608256,357389824,
%T A016290 2861214720,22898104320,183218384896,1465881288704,11727587164160,
%U A016290 93822844764160,750591347982336,6004765143465984,48038258586419200,384306618446643200,3074455146595352576,24595649968853745664
%N A016290 Expansion of g.f. 1/((1-2*x)*(1-4*x)*(1-8*x)).
%C A016290 a(n) is the number of quads in the EvenQuads-2^{n+2} deck. - _Tanya Khovanova_ and MIT PRIMES STEP senior group, Jul 02 2023
%H A016290 T. D. Noe, <a href="/A016290/b016290.txt">Table of n, a(n) for n=0..100</a>
%H A016290 Julia Crager, Felicia Flores, Timothy E. Goldberg, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker, <a href="https://arxiv.org/abs/2212.05353">How many cards should you lay out in a game of EvenQuads? A detailed study of 2-caps in AG(n,2)</a>, arXiv:2212.05353 [math.CO], 2023.
%H A016290 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-56,64).
%F A016290 G.f.: 1/((1-2*x)*(1-4*x)*(1-8*x)).
%F A016290 Difference of Gaussian binomial coefficients [ n+1, 3 ] - [ n, 3 ] (n >= 2).
%F A016290 a(n) = (2^n - 6*4^n + 8*8^n)/3. - _James R. Buddenhagen_, Dec 14 2003
%F A016290 a(n) = Sum_{0<=i,j,k,<=n; i+j+k=n} 2^i*4^j*8^k. - _Hieronymus Fischer_, Jun 25 2007
%F A016290 From _Vincenzo Librandi_, Mar 15 2011: (Start)
%F A016290 a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3) for n >= 3.
%F A016290 a(n) = 12*a(n-1) - 32*a(n-2) + 2^n with a(0)=1, a(1)=14. (End)
%F A016290 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A016290 E.g.f.: exp(2*x)*(8*exp(6*x) - 6*exp(2*x) + 1)/3.
%F A016290 a(n) = A160873(n+2)/3. (End)
%p A016290 [seq(GBC(n+1,3,2)-GBC(n,3,2), n=2..30)]; # produces A016290 (cf. A006516).
%p A016290 seq((2^n-6*4^n+8*8^n)/3, n=0..20);
%p A016290 seq(binomial(2^n,3)/4, n=2..20); # _Zerinvary Lajos_, Feb 22 2008
%t A016290 CoefficientList[Series[1/((1-2x)(1-4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-56,64},{1,14,140},30] (* _Harvey P. Dale_, Jul 23 2011 *)
%o A016290 (Magma) [(2^n-6*4^n+8*8^n)/3 : n in [0..20]]; // _Wesley Ivan Hurt_, Jul 07 2014
%Y A016290 Cf. A006516, A016152, A160873.
%K A016290 nonn,nice,easy
%O A016290 0,2
%A A016290 _N. J. A. Sloane_