A183662 - OEIS

%I #9 Apr 25 2023 13:51:05

%S 146,666,666,3254,2442,3254,16626,9990,9990,16626,87686,43986,35162,

%T 43986,87686,473586,204246,135966,135966,204246,473586,2605574,987762,

%U 563114,469146,563114,987762,2605574,14548626,4934070,2458590,1755246

%N T(n,k) = Number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock summing to 10.

%C Table starts

%C .......146.......666.......3254.....16626.....87686....473586...2605574

%C .......666......2442.......9990.....43986....204246....987762...4934070

%C ......3254......9990......35162....135966....563114...2458590..11196842

%C .....16626.....43986.....135966....469146...1755246...6990906..29275086

%C .....87686....204246.....563114...1755246...5992826..21960366..85187834

%C ....473586....987762....2458590...6990906..21960366..74549082.269462670

%C ...2605574...4934070...11196842..29275086..85187834.269462670

%C ..14548626..25308786...52793406.127755066.346364046

%C ..82214726.132730326..256308074.577190766

%C .469200306.709335282.1275989790

%H R. H. Hardin, <a href="/A183662/b183662.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical, for every row and column: a(n)=21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6).

%F The coefficient of a(n-i) is -s(7,7-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.

%F For a 0..z array with 2 X 2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i).

%e Some solutions for 4 X 3

%e ..3..3..2....2..4..3....4..1..5....2..1..4....4..3..2....2..3..2....3..1..3

%e ..0..4..1....4..0..3....2..3..1....5..2..3....3..0..5....5..0..5....4..2..4

%e ..5..1..4....4..2..5....4..1..5....3..0..5....3..4..1....1..4..1....3..1..3

%e ..2..2..3....1..3..0....3..2..2....5..2..3....1..2..3....4..1..4....1..5..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 06 2011