cp's OEIS Frontend

A227259 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227259 #21 Aug 26 2023 15:08:57
%S A227259 3,9,23,50,96,168,274,423,625,891,1233,1664,2198,2850,3636,4573,5679,
%T A227259 6973,8475,10206,12188,14444,16998,19875,23101,26703,30709,35148,
%U A227259 40050,45446,51368,57849,64923,72625,80991,90058,99864,110448,121850,134111
%N A227259 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.
%C A227259 Conjecture: a(n) is also the number of length n strings of {0,1,2} with digit sum <= 4 (holds if the empirical formula holds). - _Daniel T. Martin_, May 24 2023
%H A227259 R. H. Hardin, <a href="/A227259/b227259.txt">Table of n, a(n) for n = 1..210</a>
%F A227259 Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1.
%F A227259 G.f.: x*(3 - 6*x + 8*x^2 - 5*x^3 + x^4) / (1 - x)^5. (Conjecture from _Colin Barker_, Sep 07 2018)
%e A227259 Some solutions for n=4:
%e A227259   1 0   1 1   1 1   1 1   1 1   1 0   1 1   1 1   0 0   1 1
%e A227259   1 1   1 0   1 0   1 1   1 1   1 1   1 1   0 1   0 0   1 1
%e A227259   1 1   0 0   0 1   1 1   0 1   0 1   1 1   0 0   0 0   0 0
%e A227259   0 1   0 0   0 1   1 0   0 1   0 1   0 0   0 0   0 0   0 0
%Y A227259 Column 2 of A227263.
%Y A227259 Cf. A105163.
%K A227259 nonn
%O A227259 1,1
%A A227259 _R. H. Hardin_, Jul 04 2013