A181253 -id:A181253 - cp's OEIS frontend

A181246 Number of n X 3 binary matrices with no 2 X 2 block having four 1's.

8, 57, 417, 3032, 22077, 160697, 1169792, 8515337, 61986457, 451223152, 3284626797, 23910060017, 174050512312, 1266980540057, 9222838063377, 67136581219272, 488712965249117, 3557529413370537, 25896623226618032

Offset: 1

R. H. Hardin, Oct 10 2010

nonn

Column 3 of A181253.

R. H. Hardin, Table of n, a(n) for n=1..200

Cf. A181253.

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

Empirical g.f.: x*(8 + 9*x - 5*x^2) / (1 - 6*x - 10*x^2 + 5*x^3). - Colin Barker, Mar 26 2018

A181247 Number of n X 4 binary matrices with no 2 X 2 block having four 1's.

Original entry on oeis.org

16, 216, 3032, 42176, 587920, 8191392, 114142368, 1590466304, 22161786304, 308805072256, 4302929532288, 59957567962112, 835456401197312, 11641356029819392, 162212139560176128, 2260284639281590272

Offset: 1

R. H. Hardin, Oct 10 2010

nonn

Column 4 of A181253.

R. H. Hardin, Table of n, a(n) for n=1..200

Cf. A181253.

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

Empirical g.f.: 8*x*(2 + 7*x + x^2 - 8*x^3) / (1 - 10*x - 54*x^2 - 16*x^3 + 64*x^4). - Colin Barker, Mar 26 2018

A181248 Number of nX5 binary matrices with no 2X2 block having four 1's.

Original entry on oeis.org

32, 819, 22077, 587920, 15701273, 419045269, 11185495872, 298561305103, 7969215344753, 212714316418464, 5677773794982333, 151551208150533689, 4045206823611571168, 107974712600136074779, 2882062422625926933109

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 5 of A181253

R. H. Hardin, Table of n, a(n) for n=1..200

Empirical: 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)

A181249 Number of nX6 binary matrices with no 2X2 block having four 1's.

Original entry on oeis.org

64, 3105, 160697, 8191392, 419045269, 21418970801, 1095020802848, 55979092539545, 2861765993703849, 146298965997241152, 7479088292930771309, 382345515897175884705, 19546245848381921238016, 999242067236417336040593

Offset: 1

R. H. Hardin Oct 10 2010

nonn

Column 6 of A181253

R. H. Hardin, Table of n, a(n) for n=1..200

Empirical: 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)

A181250 Number of n X 7 binary matrices with no 2 X 2 block having four 1's.

Original entry on oeis.org

128, 11772, 1169792, 114142368, 11185495872, 1095020802848, 107224417436160, 10498818149889952, 1027999596778673856, 100657027683287334528, 9855884014448812881664, 965043721129265059674752

Offset: 1

R. H. Hardin, Oct 10 2010

nonn

Column 7 of A181253.

R. H. Hardin, Table of n, a(n) for n=1..200

Cf. A181253.

Empirical: 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).

A181251 Number of n X 8 binary matrices with no 2 X 2 block having four 1's.

Original entry on oeis.org

256, 44631, 8515337, 1590466304, 298561305103, 55979092539545, 10498818149889952, 1968910887183791359, 369248337357375835969, 69248348058920729348864, 12986755671559657328386775

Offset: 1

R. H. Hardin, Oct 10 2010

nonn

Column 8 of A181253.

R. H. Hardin, Table of n, a(n) for n=1..200

Cf. A181253.

Empirical: 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).

A181252 Number of n X 9 binary matrices with no 2 X 2 block having four 1's.

Original entry on oeis.org

512, 169209, 61986457, 22161786304, 7969215344753, 2861765993703849, 1027999596778673856, 369248337357375835969, 132633131268024896655873, 47641303155727829675539968, 17112587585474467714330327353

Offset: 1

R. H. Hardin, Oct 10 2010

nonn

Column 9 of A181253.

R. H. Hardin, Table of n, a(n) for n=1..200
Robert Israel, Maple-assisted derivation of recurrence
Robert Israel, Linear recurrence of order 48

Cf. A181253.

for i from 1 to 512 do Configs[i]:= convert(2^9+i-1,base,2)[1..9] od:
Compatible:= proc(i,j)
if `and`(seq(evalb(Configs[i][k] + Configs[i][k+1] + Configs[j][k]+Configs[j][k+1] < 4), k=1..8)) then 1 else 0 fi
end proc:
T:= Matrix(512,512,Compatible):
v:= Vector(512,1):
TV[0]:= v:
for nn from 1 to 23 do TV[nn]:= T . TV[nn-1] od:
seq(v^%T . TV[n],n=0..23); # Robert Israel, Apr 02 2020

Linear recurrence of order 48: see link. - Robert Israel, Apr 02 2020

cp's OEIS Frontend

A181246 Number of n X 3 binary matrices with no 2 X 2 block having four 1's.

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A181247 Number of n X 4 binary matrices with no 2 X 2 block having four 1's.

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A181248 Number of nX5 binary matrices with no 2X2 block having four 1's.

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A181249 Number of nX6 binary matrices with no 2X2 block having four 1's.

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A181250 Number of n X 7 binary matrices with no 2 X 2 block having four 1's.

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A181251 Number of n X 8 binary matrices with no 2 X 2 block having four 1's.

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A181252 Number of n X 9 binary matrices with no 2 X 2 block having four 1's.

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