cp's OEIS Frontend

A014235 Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 1 0 ].

%I A014235 #61 Aug 31 2023 10:50:39
%S A014235 1,2,12,128,2100,48032,1444212,54763088,2540607060,140893490432,
%T A014235 9170099291892,690117597121328,59318536757456340,5763381455631211232,
%U A014235 627402010180980401652,75942075645205885599248,10153054354133705795859540,1490544499134409408040599232
%N A014235 Number of n X n matrices with entries 0 and 1 and no 2 X 2 submatrix of form [ 1 1; 1 0 ].
%H A014235 Vincenzo Librandi, <a href="/A014235/b014235.txt">Table of n, a(n) for n = 0..200</a>
%H A014235 Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, <a href="https://arxiv.org/abs/2308.14183">Combinatorial Identities for Vacillating Tableaux</a>, arXiv:2308.14183 [math.CO], 2023. See p. 24.
%H A014235 Wenyi Feng, <a href="http://mathforum.org/kb/plaintext.jspa?messageID=58166">"counting the number of matrix"</a>, sci.math article, Feb. 5, 1997.
%H A014235 Robert Israel, <a href="http://mathforum.org/kb/plaintext.jspa?messageID=58172">"Re: counting the number of matrix"</a>, sci.math article, Feb. 5, 1997.
%H A014235 Hyeong-Kwan Ju and Seunghyun Seo, <a href="http://arxiv.org/abs/1107.1299">Enumeration of 0/1-matrices avoiding some 2x2 matrices</a>, arXiv:1107.1299 [math.CO], 2011.
%H A014235 Hyeong-Kwan Ju and Seunghyun Seo, <a href="http://dx.doi.org/10.1016/j.disc.2012.04.019">Enumeration of (0,1)-matrices avoiding some 2 X 2 matrices</a>, Discrete Math., 312 (2012), 2473-2481.
%H A014235 Susanna E. Rumsey, Stark C. Draper, and Frank R. Kschischang, <a href="https://doi.org/10.1109/TIT.2020.3040255">Information Density in Multi-Layer Resistive Memories</a>, IEEE Transactions on Information Theory (2020) Vol. 67, Issue 3, 1446-1460.
%F A014235 a(n) = Sum_{k=0..n} k! * Stirling2(n+1, k+1)^2.
%e A014235 For n = 2 the 12 matrices are all the 2 X 2 0-1 matrices except
%e A014235 [1 1]  [1 0]  [0 1]  [1 1]
%e A014235 [1 0], [1 1], [1 1], [0 1]. - _Robert Israel_, Feb 19 2015
%p A014235 f:= n -> add(k!*combinat:-stirling2(n+1,k+1)^2, k = 0 .. n):
%p A014235 seq(f(n),n=0..30); # _Robert Israel_, Feb 19 2015
%t A014235 Table[Sum[StirlingS2[n+1, k+1]^2k!, {k, 0, n}], {n, 0, 100}] (* _Emanuele Munarini_, Jul 04 2011 *)
%o A014235 (Maxima) makelist(sum(stirling2(n+1, k+1)^2*k!, k, 0, n), n, 0, 24); /* _Emanuele Munarini_, Jul 04 2011 */
%o A014235 (PARI) a(n) = sum(k=0, n, k! * stirling(n+1, k+1, 2)^2); \\ _Michel Marcus_, Feb 21 2015
%Y A014235 Cf. A023997, A048163, A111420, A213977.
%Y A014235 Row sums of A334689.
%K A014235 nonn
%O A014235 0,2
%A A014235 _Robert Israel_
%E A014235 a(0)=1 added by _Emanuele Munarini_, Jul 04 2011