cp's OEIS Frontend

A183322 T(n,k) is the number of n X k binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

%I A183322 #11 Aug 02 2025 14:26:10
%S A183322 2,3,3,5,6,5,8,13,13,8,13,27,43,27,13,21,57,124,124,57,21,34,119,377,
%T A183322 480,377,119,34,55,250,1109,1975,1975,1109,250,55,89,523,3305,7833,
%U A183322 11385,7833,3305,523,89,144,1097,9767,31428,61755,61755,31428,9767,1097,144
%N A183322 T(n,k) is the number of n X k binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.
%C A183322 Empirical: column k has a 2^k order linear recurrence (verified through k=6).
%H A183322 R. H. Hardin, <a href="/A183322/b183322.txt">Table of n, a(n) for n = 1..611</a>
%e A183322 Table starts:
%e A183322 ...2....3.....5.......8.......13.........21..........34...........55
%e A183322 ...3....6....13......27.......57........119.........250..........523
%e A183322 ...5...13....43.....124......377.......1109........3305.........9767
%e A183322 ...8...27...124.....480.....1975.......7833.......31428.......125103
%e A183322 ..13...57...377....1975....11385......61755......343035......1872913
%e A183322 ..21..119..1109....7833....61755.....455509.....3437801.....25528515
%e A183322 ..34..250..3305...31428...343035....3437801....35629548....360327392
%e A183322 ..55..523..9767..125103..1872913...25528515...360327392...4963103592
%e A183322 ..89.1097.28959..498825.10288475..190243099..3674032121..68795107993
%e A183322 .144.2297.85677.1985956.56225061.1412491505.37171418048.947461430557
%e A183322 Some solutions for 7 X 3:
%e A183322 ..1..1..1....0..0..0....1..1..0....1..1..0....0..0..0....0..0..1....0..0..0
%e A183322 ..1..1..1....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....0..1..1
%e A183322 ..0..0..1....0..0..1....1..1..1....0..0..0....1..1..1....1..1..1....0..1..1
%e A183322 ..1..1..1....0..1..1....1..1..0....1..1..0....1..1..0....0..0..1....1..1..1
%e A183322 ..1..1..1....1..1..0....0..0..0....1..1..0....1..1..0....0..1..1....1..1..1
%e A183322 ..0..0..1....1..1..0....0..0..1....0..1..1....1..1..0....1..1..1....0..1..1
%e A183322 ..1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....0..1..1
%K A183322 nonn,tabl
%O A183322 1,1
%A A183322 _R. H. Hardin_, Jan 03 2011