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 A016152 #59 Aug 21 2025 22:01:14
%S A016152 0,1,12,112,960,7936,64512,520192,4177920,33488896,268173312,
%T A016152 2146435072,17175674880,137422176256,1099444518912,8795824586752,
%U A016152 70367670435840,562945658454016,4503582447501312,36028728299487232
%N A016152 a(n) = 4^(n-1)*(2^n-1).
%C A016152 Numbers whose binary representation is the concatenation of n digits 1 and 2(n-1) digits 0, for n>0. (See A147816.) - _Omar E. Pol_, Nov 13 2008
%C A016152 a(n) is the number of lattices L in Z^n such that the quotient group Z^n / L is C_8. - _Álvar Ibeas_, Nov 29 2015
%C A016152 a(n) is a maximum number of intercalates in a Latin square of order 2^n (see A092237). - _Eduard I. Vatutin_, Apr 30 2025
%H A016152 Vincenzo Librandi, <a href="/A016152/b016152.txt">Table of n, a(n) for n = 0..140</a>
%H A016152 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/evatutin_max_i_ls_2_pow_n.pdf">Example of Latin squares of order 2^n with maximum number of intercalates</a>.
%H A016152 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-32).
%F A016152 From _Barry E. Williams_, Jan 17 2000: (Start)
%F A016152 a(n) = ((8^(n+1)) - 4^(n+1))/4.
%F A016152 a(n) = 12a(n-1) - 32a(n-2), n>0; a(0)=1. (End)
%F A016152 a(n) = (4^(n-1))*Stirling2(n+1, 2), n>=0, with Stirling2(n, m)=A008277(n, m).
%F A016152 a(n) = -4^(n-1) + 2*8^(n-1).
%F A016152 E.g.f. for a(n+1), n>=0: d^2/dx^2((((exp(4*x)-1)/4)^2)/2!) = -exp(4*x) + 2*exp(8*x).
%F A016152 G.f.: x/((1-4*x)*(1-8*x)).
%F A016152 ((6+sqrt4)^n - (6-sqrt4)^n)/4 in Fibonacci form. Offset 1. a(3)=112. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008
%F A016152 a(n) + A160873(n) + A006096(n) = A006096(n+2), for n > 2. - _Álvar Ibeas_, Nov 29 2015
%F A016152 Sum_{n>0} 1/a(n) = 4*E - 16/3, where E is the Erdős-Borwein constant (A065442). - _Peter McNair_, Dec 19 2022
%t A016152 Table[4^(n - 1) (2^n - 1), {n, 0, 19}] (* _Michael De Vlieger_, Nov 30 2015 *)
%o A016152 (Sage) [lucas_number1(n,12,32) for n in range(0, 20)] # _Zerinvary Lajos_, Apr 27 2009
%o A016152 (Magma) [4^(n-1)*(2^n-1): n in [0..40]]; // _Vincenzo Librandi_, Apr 26 2011
%o A016152 (PARI) a(n)=4^(n-1)*(2^n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A016152 (PARI) my(x='x+O('x^30)); concat(0, Vec(x/((1-4*x)*(1-8*x)))) \\ _Altug Alkan_, Dec 04 2015
%Y A016152 Second column of triangle A075499.
%Y A016152 Cf. A019677, A147538, A147816.
%Y A016152 Cf. A065442, A092237.
%K A016152 nonn,easy,changed
%O A016152 0,3
%A A016152 _N. J. A. Sloane_