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

1,1

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

Links

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

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)

Example

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

Crossrefs

Column 2 of A227263.

Cf. A105163.

Sequence in context: A147271 A230119 A146693 * A064551 A005783 A263330

Adjacent sequences: A227256 A227257 A227258 * A227260 A227261 A227262

Keyword

nonn

Author

R. H. Hardin, Jul 04 2013

Status

approved