A183782 - OEIS

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A183782

T(n,k) = half the number of (n+1) X (k+1) binary arrays with no 2 X 2 subblock having exactly 2 ones.

5, 13, 13, 33, 47, 33, 85, 161, 161, 85, 217, 567, 730, 567, 217, 557, 1969, 3435, 3435, 1969, 557, 1425, 6887, 15887, 21935, 15887, 6887, 1425, 3653, 24001, 74148, 136843, 136843, 74148, 24001, 3653, 9353, 83799, 344483, 864671, 1146964, 864671, 344483

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OFFSET

1,1

COMMENTS

All columns (or rows) are linear recurrences with constant coefficients with the order of the recurrence <= A005418(k+1). For columns up to k=6, the only case where the order is strictly less than this upper bound is for column 4. - Andrew Howroyd, Jan 09 2025

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..364

EXAMPLE

Table starts:

5 13 33 85 217 557 1425

13 47 161 567 1969 6887 24001

33 161 730 3435 15887 74148 344483

85 567 3435 21935 136843 864671 5431499

217 1969 15887 136843 1146964 9764363 82573675

557 6887 74148 864671 9764363 112439612 1284649009

1425 24001 344483 5431499 82573675 1284649009 19815396763

3653 83799 1604473 34228999 701022093 14750484447 307446383061