A139810 -id:A139810 - cp's OEIS frontend

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

R. H. Hardin, Oct 10 2010

			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

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

Diagonal is A139810.

Column 2 is A125145.

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)+47046600*a(n-6)-471525808*a(n-7)+1012118640*a(n-8)+2396096576*a(n-9)-9445394304*a(n-10)-4382776896*a(n-11)+29415041536*a(n-12)+8676097024*a(n-13)-36065068032*a(n-14)-14871987200*a(n-15)+10138337280*a(n-16)+2907136000*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)+5948333641*a(n-6)-25692714697*a(n-7)-932093986319*a(n-8)+9749317949468*a(n-9)+6293344318720*a(n-10)-400364584466276*a(n-11)+544975615003201*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)

A140304 Number of n X n binary matrices with no more than one 1 in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 5, 10, 60, 437, 2875, 36409, 704468, 14783959, 461938624, 22488554884, 1378748967395, 115759328877461, 14408020654986447, 2435526103569141336, 559083220302137929773, 182904062593977747117174, 83283166161035345074485948, 52012981990902321891650583747, 45449967513840995133445585972949

Offset: 0

R. H. Hardin, May 27 2008

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..23
R. J. Mathar, Tiling n X m rectangles with 1 X 1 and s X s squares, arXiv:1609.03964 [math.CO], 2016.

Cf. A139810. Row sums of A276171.

$RecursionLimit = 10^4;
b[n_, l_] := b[n, l] = Module[{k, m}, m = Min[l]; Which[n < 3, 1, m > 0, b[n - m, l - m], True, k = 1; While[l[[k]] > 0, k++]; b[n, ReplacePart[l, k -> 1]] + Expand[If[k + 1 < Length[l] && l[[k + 1 ;; k + 2]] == {0, 0}, b[n, ReplacePart[l, {k -> 3, k + 1 -> 3, k + 2 -> 3}]]*x, 0]]]];
a[n_] := a[n] = Function[p, Sum[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n + 2, Table[0, n + 2]]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 15}] (* Jean-François Alcover, Nov 11 2017, after Alois P. Heinz *)

A140314 Number of n X n binary matrices containing no more than two 1's in any 2 X 2 subblock.

Original entry on oeis.org

1, 2, 11, 195, 8969, 1232795, 471487297, 516844071813, 1603508113421239, 14148460147460008963, 354360105981877906958557, 25210728065407321182797745205, 5093486498660018140333056634922039

Offset: 0

R. H. Hardin, May 25 2008

nonn

No more than 1 1 in any 2 X 2 subblock gives A063443.

No more than 3 1's in any 2 X 2 subblock gives A139810.

R. H. Hardin, May 25 2008, Table of n, a(n) for n = 0..15

Cf. A063443, A139810.

A140311 Number of n X n binary matrices containing no more than eight 1s in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 16, 511, 65089, 33066176, 66993993728, 541344347284385, 17445985904048740529, 2242340146792849255134720, 1149454044962768236388517543936, 2349989206497316681704056634171383423

Offset: 0

R. H. Hardin, May 27 2008

nonn

R. H. Hardin, May 27 2008, Table of n, a(n) for n = 0..15

Cf. A139810.

A140305 Number of n X n binary matrices containing no more than two 1s in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 11, 46, 824, 27178, 1020762, 102044420, 20297233254, 6218446852487, 3906297811846469, 4829512709969500388, 10588146860457194561192, 44163637535605999104548698

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

A140306 Number of n X n binary matrices containing at most three 1's in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 15, 130, 4852, 456904, 73948482, 35616138799, 43142990277818, 115017363443317954, 771239506285440035857

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

A140307 Number of n X n binary matrices containing at most four 1's in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 16, 256, 15982, 3082378, 1476568000, 2280441045555, 10599616558936358, 140380164790852384033

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

A140308 Number of n X n binary matrices containing no more than five 1s in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 16, 382, 33940, 10537021, 10478502929, 36396596300106, 433087032815881242, 17394297682298725368562

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

A140309 Number of n X n binary matrices containing no more than six 1s in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 16, 466, 51512, 21425198, 32840182186, 188637643581570, 4048457379398984078, 323937479341259299455434, 96758393657902322435446080112

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

A140310 Number of n X n binary matrices containing no more than seven 1s in any 3 X 3 sub-block.

Original entry on oeis.org

1, 2, 16, 502, 61788, 29829353, 56365481377, 417452923577327, 12115365147171963168, 1377708150938828616858899, 613888995116283293759860580312, 1071847970096627711898648239726154442

Offset: 0

R. H. Hardin, May 27 2008

nonn

Cf. A139810.

cp's OEIS Frontend

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

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A140304 Number of n X n binary matrices with no more than one 1 in any 3 X 3 sub-block.

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A140314 Number of n X n binary matrices containing no more than two 1's in any 2 X 2 subblock.

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A140311 Number of n X n binary matrices containing no more than eight 1s in any 3 X 3 sub-block.

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A140305 Number of n X n binary matrices containing no more than two 1s in any 3 X 3 sub-block.

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A140306 Number of n X n binary matrices containing at most three 1's in any 3 X 3 sub-block.

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A140307 Number of n X n binary matrices containing at most four 1's in any 3 X 3 sub-block.

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A140308 Number of n X n binary matrices containing no more than five 1s in any 3 X 3 sub-block.

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A140309 Number of n X n binary matrices containing no more than six 1s in any 3 X 3 sub-block.

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A140310 Number of n X n binary matrices containing no more than seven 1s in any 3 X 3 sub-block.

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