A181253 T(n,k)=Number of nXk binary matrices with no 2X2 block having four 1's.

2, 4, 4, 8, 15, 8, 16, 57, 57, 16, 32, 216, 417, 216, 32, 64, 819, 3032, 3032, 819, 64, 128, 3105, 22077, 42176, 22077, 3105, 128, 256, 11772, 160697, 587920, 587920, 160697, 11772, 256, 512, 44631, 1169792, 8191392, 15701273, 8191392, 1169792, 44631, 512

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn
• tabl

Examples

			Table starts
....2......4.........8...........16..............32.................64
....4.....15........57..........216.............819...............3105
....8.....57.......417.........3032...........22077.............160697
...16....216......3032........42176..........587920............8191392
...32....819.....22077.......587920........15701273..........419045269
...64...3105....160697......8191392.......419045269........21418970801
..128..11772...1169792....114142368.....11185495872......1095020802848
..256..44631...8515337...1590466304....298561305103.....55979092539545
..512.169209..61986457..22161786304...7969215344753...2861765993703849
.1024.641520.451223152.308805072256.212714316418464.146298965997241152
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..721

Crossrefs

Diagonal is A139810.

Column 2 is A125145.

Formula

Empirical column 1: a(n)=2*a(n-1)

Empirical column 2: a(n)=3*a(n-1)+3*a(n-2)

Empirical column 3: a(n)=6*a(n-1)+10*a(n-2)-5*a(n-3)

Empirical column 4: a(n)=10*a(n-1)+54*a(n-2)+16*a(n-3)-64*a(n-4)

Empirical column 5: a(n)=20*a(n-1)+188*a(n-2)-192*a(n-3)-1660*a(n-4)+2804*a(n-5)-507*a(n-6)-624*a(n-7)

Empirical column 6: a(n)=33*a(n-1)+908*a(n-2)+1687*a(n-3)-37947*a(n-4)-16572*a(n-5)+513993*a(n-6)-663729*a(n-7)-486540*a(n-8)+617409*a(n-9)+191835*a(n-10)-49140*a(n-11)

Empirical column 7: a(n)=68*a(n-1)+3106*a(n-2)-10300*a(n-3)-731184*a(n-4)+3930848*a(n-5)[phone]*a(n-6)-471525808*a(n-7)[phone]*a(n-8)[phone]*a(n-9)-9445394304*a(n-10)-4382776896*a(n-11)[phone]*a(n-12)[phone]*a(n-13)-36065068032*a(n-14)-14871987200*a(n-15)[phone]*a(n-16)[phone]*a(n-17)-1119682560*a(n-18)

Empirical column 8: a(n)=113*a(n-1)+13879*a(n-2)+91506*a(n-3)-13567062*a(n-4)-45766270*a(n-5)[phone]*a(n-6)-25692714697*a(n-7)-932093986319*a(n-8)[phone]*a(n-9)[phone]*a(n-10)-400364584466276*a(n-11)[phone]*a(n-12)+8011657063605359*a(n-13)-12237642139437047*a(n-14)-98976024373360414*a(n-15)+87321080164809042*a(n-16)+743714645681446194*a(n-17)-21941742884172873*a(n-18)-2838216189512832023*a(n-19)-1559534908222727729*a(n-20)+4451110188283146640*a(n-21)+3110756142589939204*a(n-22)-3806251587192837456*a(n-23)-2258950594106495040*a(n-24)+1998716044109621760*a(n-25)+565195437997056000*a(n-26)-541032812384256000*a(n-27)+28184753405952000*a(n-28)+19493777571840000*a(n-29)