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A228482 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally. 8
1, 1, 1, 2, 2, 2, 3, 4, 4, 3, 5, 9, 14, 9, 5, 8, 19, 41, 41, 19, 8, 13, 41, 127, 172, 127, 41, 13, 21, 88, 386, 728, 728, 386, 88, 21, 34, 189, 1181, 3084, 4354, 3084, 1181, 189, 34, 55, 406, 3605, 13050, 25699, 25699, 13050, 3605, 406, 55, 89, 872, 11013, 55252, 152373 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Table starts

..1...1.....2......3.......5.........8.........13..........21............34

..1...2.....4......9......19........41.........88.........189...........406

..2...4....14.....41.....127.......386.......1181........3605.........11013

..3...9....41....172.....728......3084......13050.......55252........233875

..5..19...127....728....4354.....25699.....152373......902042.......5342712

..8..41...386...3084...25699....211588....1748684....14433982.....119188751

.13..88..1181..13050..152373...1748684...20185842...232542935....2680777055

.21.189..3605..55252..902042..14433982..232542935..3737615288...60122232373

.34.406.11013.233875.5342712.119188751.2680777055.60122232373.1349721589622

Same recurrences as A228285 except in addition this smaller one for k=5

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1333

FORMULA

Recurrences for column k:

k=1: a(n) = a(n-1) +a(n-2)

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

k=3: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) -a(n-5)

k=4: a(n) = a(n-1) +10*a(n-2) +15*a(n-3) +4*a(n-4) -6*a(n-5) -a(n-6) +3*a(n-7) -a(n-8)

k=5: a(n) = 3*a(n-1) +15*a(n-2) +16*a(n-3) -11*a(n-4) -20*a(n-5) +19*a(n-6) -8*a(n-7) +a(n-9)

k=6: a(n) = a(n-1) +42*a(n-2) +147*a(n-3) +70*a(n-4) -478*a(n-5) -449*a(n-6) +1199*a(n-7) +732*a(n-8) -2727*a(n-9) +659*a(n-10) +3827*a(n-11) -5776*a(n-12) +3926*a(n-13) -1152*a(n-14) -148*a(n-15) +154*a(n-16) +32*a(n-17) -29*a(n-18) -6*a(n-19) +3*a(n-20) +a(n-21)

k=7: a(n) = a(n-1) +85*a(n-2) +432*a(n-3) +192*a(n-4) -3711*a(n-5) -5096*a(n-6) +21164*a(n-7) +27340*a(n-8) -112654*a(n-9) -37244*a(n-10) +477721*a(n-11) -464722*a(n-12) -897815*a(n-13) +3102284*a(n-14) -4149918*a(n-15) +2761082*a(n-16) -138325*a(n-17) -1353257*a(n-18) +942033*a(n-19) +64683*a(n-20) -365483*a(n-21) +80904*a(n-22) +92350*a(n-23) -27097*a(n-24) -23292*a(n-25) +2585*a(n-26) +5635*a(n-27) +1405*a(n-28) -561*a(n-29) -545*a(n-30) -173*a(n-31) -14*a(n-32) +5*a(n-33) +a(n-34)

EXAMPLE

Some solutions for n=4 k=4

..1..0..0..1....1..0..1..0....1..0..0..1....1..0..1..0....1..0..1..0

..0..0..0..0....0..0..0..1....0..1..0..0....0..0..0..0....0..0..0..0

..0..0..0..1....0..0..0..0....0..0..1..0....0..1..0..0....0..0..0..0

..0..0..0..0....0..1..0..0....0..0..0..1....0..0..1..0....1..0..0..0

CROSSREFS

Column 1 is A000045

Column 2 is A078039(n-1).

Cf. A228476-A228481, A228277-A228285, A226444.

Sequence in context: A060243 A054225 A322210 * A091822 A173022 A060973

Adjacent sequences:  A228479 A228480 A228481 * A228483 A228484 A228485

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Aug 22 2013

STATUS

approved

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Last modified October 15 15:13 EDT 2019. Contains 328030 sequences. (Running on oeis4.)