cp's OEIS Frontend

A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207391 #7 Jul 22 2025 20:21:40
%S A207391 2,4,4,6,16,6,9,36,36,8,14,81,98,64,10,21,196,271,200,100,12,31,441,
%T A207391 834,643,350,144,14,46,961,2307,2356,1271,556,196,16,68,2116,6115,
%U A207391 7561,5348,2239,826,256,18,100,4624,16544,23071,19319,10570,3641,1168,324,20,147
%N A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207391 Table starts
%C A207391 ..2...4....6....9....14.....21.....31......46.......68......100.......147
%C A207391 ..4..16...36...81...196....441....961....2116.....4624....10000.....21609
%C A207391 ..6..36...98..271...834...2307...6115...16544....44250...116526....307117
%C A207391 ..8..64..200..643..2356...7561..23071...72410...223804...678174...2060069
%C A207391 .10.100..350.1271..5348..19319..65955..232892...806886..2731598...9282799
%C A207391 .12.144..556.2239.10570..42167.158217..616386..2348280..8718366..32527713
%C A207391 .14.196..826.3641.18972..82477.335915.1424240..5887228.23664574..95673277
%C A207391 .16.256.1168.5581.31710.148743.651531.2975974.13215696.56972122.247183399
%H A207391 R. H. Hardin, <a href="/A207391/b207391.txt">Table of n, a(n) for n = 1..480</a>
%F A207391 Empirical for column k:
%F A207391 k=1: a(n) = 2*n
%F A207391 k=2: a(n) = 4*n^2
%F A207391 k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
%F A207391 k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
%F A207391 k=5: a(n) = (2/15)*n^5 + (55/12)*n^4 + (101/6)*n^3 + (5/12)*n^2 - (299/30)*n + 2
%F A207391 k=6: a(n) = (1/36)*n^6 + (113/60)*n^5 + (151/9)*n^4 + (95/4)*n^3 - (605/36)*n^2 - (229/30)*n + 3
%F A207391 k=7: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3
%e A207391 Some solutions for n=4 k=3
%e A207391 ..1..0..0....0..0..0....0..1..1....1..1..1....1..1..1....1..0..1....1..0..1
%e A207391 ..0..0..0....0..1..1....1..1..0....1..1..1....1..0..1....1..0..1....0..1..1
%e A207391 ..1..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..1....0..1..1
%e A207391 ..0..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..1....0..1..1
%Y A207391 Column 1 is A004275(n+1)
%Y A207391 Column 2 is A016742
%Y A207391 Column 3 is A207106
%Y A207391 Column 4 is A207107
%Y A207391 Row 1 is A038718(n+2)
%Y A207391 Row 2 is A207069
%K A207391 nonn,tabl
%O A207391 1,1
%A A207391 _R. H. Hardin_ Feb 17 2012