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 A126644 #25 Nov 22 2022 06:05:07
%S A126644 4,16,58,196,634,1996,6178,18916,57514,174076,525298,1582036,4758394,
%T A126644 14299756,42948418,128943556,387027274,1161475036,3485211538,
%U A126644 10457207476,31374768154,94130595916,282404370658,847238277796
%N A126644 a(n) = 3*3^n - 3*2^n + 1.
%C A126644 Previous name was: a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4,5,6 and at least one of digits 7,8,9.
%C A126644 Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is a proper subset of y or y is a proper subset of x, 1) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 2) x equals y. Then a(n) = |R|. [_Ross La Haye_, Mar 19 2009]
%H A126644 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H A126644 Ross La Haye, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/LaHaye/lahaye5.html">Binary Relations on the Power Set of an n-Element Set</a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
%H A126644 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A126644 a(n) = 3*3^n - 3*2^n + 1.
%F A126644 a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3). G.f.: -2*x*(3*x^2-4*x+2) / ((x-1)*(2*x-1)*(3*x-1)). [_Colin Barker_, Dec 10 2012]
%F A126644 a(n) = 3*A001047(n) + 1. - _Hugo Pfoertner_, Nov 22 2022
%e A126644 a(8) = 18916.
%p A126644 f:=n->3*3^n-3*2^n+1;
%t A126644 LinearRecurrence[{6,-11,6},{4,16,58},30] (* _Harvey P. Dale_, Sep 14 2018 *)
%o A126644 (PARI) a(n) = 3*3^n - 3*2^n + 1; \\ _Michel Marcus_, Nov 30 2015
%Y A126644 Cf. A001047, A125630, A125948, A125947, A125946, A125945, A125940, A125909, A125908, A125880, A125897, A125904, A125858.
%K A126644 nonn,easy
%O A126644 1,1
%A A126644 Aleksandar M. Janjic and _Milan Janjic_, Feb 08 2007
%E A126644 New name from _Hugo Pfoertner_, Nov 22 2022