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.

3, 9, 23, 50, 96, 168, 274, 423, 625, 891, 1233, 1664, 2198, 2850, 3636, 4573, 5679, 6973, 8475, 10206, 12188, 14444, 16998, 19875, 23101, 26703, 30709, 35148, 40050, 45446, 51368, 57849, 64923, 72625, 80991, 90058, 99864, 110448, 121850, 134111

Offset: 1

Author

R. H. Hardin, Jul 04 2013

Keywords

• nonn

Comments

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

Examples

			Some solutions for n=4:
  1 0   1 1   1 1   1 1   1 1   1 0   1 1   1 1   0 0   1 1
  1 1   1 0   1 0   1 1   1 1   1 1   1 1   0 1   0 0   1 1
  1 1   0 0   0 1   1 1   0 1   0 1   1 1   0 0   0 0   0 0
  0 1   0 0   0 1   1 0   0 1   0 1   0 0   0 0   0 0   0 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 2 of A227263.

Cf. A105163.

Formula

Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1.

G.f.: x*(3 - 6*x + 8*x^2 - 5*x^3 + x^4) / (1 - x)^5. (Conjecture from Colin Barker, Sep 07 2018)