cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 12 results. Next

A189612 Number of n X 4 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

12, 144, 1164, 8496, 65160, 515560, 4075336, 32031600, 251533888, 1976926440, 15543816656, 122208548968, 960755182696, 7553047614920, 59379727197728, 466827426445200, 3670067881137352, 28853031765433504, 226834374728410104
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Column 4 of A189617.

Examples

			Some solutions for 3 X 4
..1..1..1..1....0..1..1..0....1..1..0..0....1..0..0..0....1..1..1..0
..1..1..0..1....1..1..0..1....1..1..1..0....1..0..1..1....0..1..1..0
..0..0..1..1....1..0..1..1....1..1..1..0....1..1..0..1....0..1..1..1
		

Crossrefs

Cf. A189617.

Formula

Empirical: a(n) = 12*a(n-1) -29*a(n-2) -69*a(n-3) +512*a(n-4) -1626*a(n-5) +60*a(n-6) +9924*a(n-7) -9708*a(n-8) +1120*a(n-9) +1064*a(n-10) -73360*a(n-11) +46560*a(n-12) +40960*a(n-13) +31616*a(n-14) +147456*a(n-15) -64000*a(n-16) -110592*a(n-17) -16384*a(n-18) -32768*a(n-19).

A189613 Number of nX5 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

21, 441, 5238, 50024, 532565, 6110500, 69943253, 783072552, 8759983583, 98440457351, 1108879339651, 12480666817260, 140421583259356, 1580016922218493, 17782853849081975, 200149452833682454
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 5 of A189617

Examples

			Some solutions for 3X5
..0..1..1..0..0....0..1..1..0..1....1..1..0..1..1....0..0..0..0..1
..1..0..0..1..1....1..1..1..1..0....1..0..0..1..1....0..0..0..1..1
..1..1..1..0..0....0..1..1..0..1....1..1..0..1..1....1..1..0..0..1
		

Formula

Empirical: a(n) = 16*a(n-1) -47*a(n-2) -126*a(n-3) +2471*a(n-4) -25560*a(n-5) +55367*a(n-6) -83579*a(n-7) -124019*a(n-8) +7300122*a(n-9) -7365184*a(n-10) -599459*a(n-11) -31727197*a(n-12) -754040572*a(n-13) +142951670*a(n-14) +953676928*a(n-15) +1891140440*a(n-16) +29553742000*a(n-17) +9452004592*a(n-18) -65219737520*a(n-19) -36827703408*a(n-20) -187343367808*a(n-21) -114093863744*a(n-22) +354967210752*a(n-23) +176354022912*a(n-24) +450092691456*a(n-25) +319703132160*a(n-26) -570350149632*a(n-27) -92906913792*a(n-28) +66527690752*a(n-29)

A189614 Number of nX6 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

37, 1369, 25046, 357323, 6204967, 118571483, 2239578131, 41236726541, 764615054191, 14279876468131, 267312630925466, 4997721311916752, 93457924722647556, 1748307417599408282, 32716532907276172258
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 6 of A189617

Examples

			Some solutions for 3X6
..1..1..1..0..0..1....0..1..1..1..0..1....1..1..1..1..0..0....0..1..1..1..1..0
..1..1..1..1..0..1....1..0..0..1..1..1....0..1..1..0..0..1....0..0..1..1..1..1
..0..1..1..1..0..1....1..1..1..1..0..0....1..0..1..1..1..0....1..1..1..1..1..1
		

Formula

Empirical: a(n) = 34*a(n-1) -273*a(n-2) -1543*a(n-3) +40714*a(n-4) -423436*a(n-5) +1891925*a(n-6) +11382071*a(n-7) -137777519*a(n-8) +619526969*a(n-9) -3051912182*a(n-10) -5331883039*a(n-11) +135922588255*a(n-12) -446254846360*a(n-13) +1981282037563*a(n-14) -1352440675161*a(n-15) -63730745022070*a(n-16) +182009632853615*a(n-17) -510273118788064*a(n-18) +873874282660350*a(n-19) +15966677554244869*a(n-20) -45068335032919311*a(n-21) +42001589746288853*a(n-22) -23954650833475138*a(n-23) -1965823312269953297*a(n-24) +4736772668657102402*a(n-25) -321838206410754775*a(n-26) -3490525798170821031*a(n-27) +131002473077969472436*a(n-28) -289945050533230354231*a(n-29) -124815760116334868152*a(n-30) +449941206981236546960*a(n-31) -5395910249931963713912*a(n-32) +10866779447842416353719*a(n-33) +11536849320735754902544*a(n-34) -24740377281791788305745*a(n-35) +120359108489170883290616*a(n-36) -238998119217361365808602*a(n-37) -418557772218732315039599*a(n-38) +600992594569779874021215*a(n-39) -1110268418593691902568994*a(n-40) +3730643584123938194728732*a(n-41) +6812552779026261797112419*a(n-42) -9687867356897283878491420*a(n-43) -1309838312543142731191598*a(n-44) -37543181860019927047383931*a(n-45) -48534998059287354072917506*a(n-46) +99166902904276678472995901*a(n-47) +66092631822176453939343434*a(n-48) +203207577442914090135690681*a(n-49) +189728844012466915601319054*a(n-50) -506168757194069244271739920*a(n-51) -359051684776210111121589893*a(n-52) -701652271809517681542984241*a(n-53) -709279979479064531996620449*a(n-54) +1324314785683074992771896760*a(n-55) +1546214833162415051904472249*a(n-56) +1926047913967698886510046700*a(n-57) +1324880649273257726226280142*a(n-58) -2485235229893697449784455071*a(n-59) -3469949260001674146745024738*a(n-60) -2669195943636818688103802021*a(n-61) -1316545684560634297023878714*a(n-62) +2690902906778032920892306556*a(n-63) +4133138157346156285018328868*a(n-64) +1833419575967533187478331078*a(n-65) +554663207333170904556676460*a(n-66) -1480074780643074473150795768*a(n-67) -2560708729238565401170287348*a(n-68) -578101303301196218417346064*a(n-69) +120143793170057270480693456*a(n-70) +306395026593453930061565088*a(n-71) +714642471292967891376788224*a(n-72) +123891781631763400927121408*a(n-73) -113050195010112502389054976*a(n-74) -10326274496355022765406720*a(n-75) -74415569321357657952191488*a(n-76) -26673454014229123407939584*a(n-77) +19388901072695556485099520*a(n-78) +2162203845803452120702976*a(n-79) -488101981191658934452224*a(n-80) +1188297076180688388521984*a(n-81) -319125673972066725003264*a(n-82) -189181015073839552659456*a(n-83) +14272540787066622967808*a(n-84) -5883883284335293366272*a(n-85) +5195966030810541195264*a(n-86) +2520091923308397723648*a(n-87) +38264251505323278336*a(n-88) +69418617620825899008*a(n-89) -4272458154689691648*a(n-90)

A189615 Number of nX7 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

65, 4225, 116100, 2482591, 68121839, 2076231513, 61652076124, 1785011303305, 52081392909734, 1531637258052071, 45087524679984918, 1325492265359151122, 38967877720497094747, 1146070566293713302197, 33712980614275859943483
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 7 of A189617

Examples

			Some solutions for 3X7
..0..0..1..1..1..0..1....0..0..1..1..0..1..1....1..1..1..1..0..0..1
..1..0..1..1..0..0..0....0..0..0..0..0..0..1....1..0..1..1..0..0..0
..1..1..0..1..1..1..0....1..0..1..1..1..1..0....1..0..1..1..1..1..1
		

A189616 Number of nX8 binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

114, 12996, 526418, 15915001, 636683482, 28823835852, 1256763617551, 52939317116118, 2243913970341972, 96114581661833896, 4121472431976051699, 176378174243580691358, 7545272457917436835785, 322957852724963531996423
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 8 of A189617

Examples

			Some solutions for 3X8
..0..0..0..0..0..1..1..0....0..0..1..1..1..0..0..0....0..0..0..0..1..1..1..1
..0..0..0..0..1..1..0..1....1..0..1..1..0..0..0..1....1..1..0..0..1..1..0..1
..0..1..1..0..0..1..1..1....0..0..1..1..0..0..1..1....1..1..1..1..0..1..1..0
		

A189618 Number of 3Xn binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

8, 64, 292, 1164, 5238, 25046, 116100, 526418, 2403976, 11065442, 50854642, 233077382, 1068505272, 4902990456, 22498260976, 103204910914, 473409837692, 2171794653270, 9963444579674, 45707359388096, 209680588779494
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Row 3 of A189617

Examples

			Some solutions for 3X3
..0..0..1....0..1..1....1..0..1....0..0..1....1..1..0....0..1..1....1..1..0
..0..0..0....0..0..0....0..1..1....1..1..0....1..0..0....1..0..1....0..0..0
..0..1..1....1..0..1....0..1..1....0..0..1....1..1..1....0..0..0....1..1..0
		

Formula

Empirical: a(n) = 5*a(n-1) -8*a(n-2) +24*a(n-3) +35*a(n-4) -90*a(n-5) +103*a(n-6) -92*a(n-7) -479*a(n-8) +312*a(n-9) +411*a(n-10) -97*a(n-11) +212*a(n-12) -154*a(n-13) -300*a(n-14) +72*a(n-15) -175*a(n-16) +42*a(n-17) -20*a(n-18) +4*a(n-19)

A189619 Number of 4 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

16, 256, 1723, 8496, 50024, 357323, 2482591, 15915001, 100745265, 655633882, 4322765564, 28292943180, 183873191611, 1195974189947, 7802581300173, 50931021729006, 332106212299242, 2164490825527781, 14110729853099870
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Examples

			Some solutions for 4 X 3:
  1 1 1   0 0 0   1 1 0   1 1 0   1 1 0   1 1 0   0 0 1
  1 0 1   1 0 0   0 0 1   1 0 1   1 0 1   1 0 1   0 1 1
  1 1 1   1 0 1   0 0 0   1 0 0   1 0 0   0 0 0   1 0 1
  0 1 1   1 1 0   1 1 1   0 1 1   1 0 0   1 1 0   1 0 1
		

Crossrefs

Row 4 of A189617.

Programs

  • Maple
    Configs:= [seq(convert(n,base,2)[1..8],n=2^8..2^9-1)]:
    Compatible:= proc(i,j) local Xi,Xj,k;
    Xi:= Configs[i]; Xj:= Configs[j];
    if Xi[5..8] <> Xj[1..4] then return 0 fi;
    if Xi[1]=0 and ((Xi[5]=1 and Xj[5]=0) or (Xi[6]=1 and Xj[7]=0)) then return 0 fi;
    if Xi[2]=0 and ((Xi[6]=1 and Xj[6]=0) or (Xi[7]=1 and Xj[8]=0)) then return 0 fi;
    if Xi[3]=0 and ((Xi[6]=1 and Xj[5]=0) or (Xi[7]=1 and Xj[7]=0)) then return 0 fi;
    if Xi[4]=0 and ((Xi[7]=1 and Xj[6]=0) or (Xi[8]=1 and Xj[8]=0)) then return 0 fi;
    1
    end proc:
    T:= Matrix(256,256,Compatible):
    Tu[0]:= u:
    for nn from 1 to 30 do Tu[nn]:= T . Tu[nn-1] od:
    [16, seq(u^%T . Tu[n],n=0..30)]; # Robert Israel, Oct 20 2019

Formula

Empirical: a(n) = 8*a(n-1) -14*a(n-2) +10*a(n-3) +258*a(n-4) -737*a(n-5) -1502*a(n-6) +1780*a(n-7) +8033*a(n-8) -4800*a(n-9) -30115*a(n-10) +54016*a(n-11) -79554*a(n-12) -215482*a(n-13) +787373*a(n-14) -626468*a(n-15) -426934*a(n-16) +3545678*a(n-17) -6093224*a(n-18) +8409993*a(n-19) -6556066*a(n-20) +986540*a(n-21) -4549030*a(n-22) +9400135*a(n-23) -23776243*a(n-24) +29721357*a(n-25) -36187856*a(n-26) +30281962*a(n-27) -31933555*a(n-28) +10845312*a(n-29) +5786415*a(n-30) +7694508*a(n-31) +5236176*a(n-32) -9921669*a(n-33) -713908*a(n-34) +1520657*a(n-35) -3672439*a(n-36) +1127159*a(n-37) +4759522*a(n-38) -673175*a(n-39) -2818276*a(n-40) -151046*a(n-41) +1043153*a(n-42) +59137*a(n-43) -154754*a(n-44) -24424*a(n-45) +16833*a(n-46) +160*a(n-47) -631*a(n-48) -60*a(n-49) +4*a(n-50).
Empirical formula verified (see link). - Robert Israel, Oct 20 2019

A189620 Number of 5 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

32, 1024, 10327, 65160, 532565, 6204967, 68121839, 636683482, 5785616468, 56137313726, 563010113815, 5529846867761, 53193183705288, 513158091226513, 5003028394342619, 48867656731556592, 475282571037202342
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Row 5 of A189617.

Examples

			Some solutions for 5 X 3:
  0 0 0   0 0 0   1 0 1   0 0 0   0 1 1   0 1 1   0 0 0
  1 0 1   0 1 1   1 1 1   0 0 1   0 0 1   0 0 0   0 0 0
  0 0 1   1 1 1   1 1 1   0 0 0   1 0 0   0 0 1   0 0 1
  1 1 0   0 0 1   1 0 0   1 0 1   1 0 0   0 0 1   1 0 0
  0 0 1   0 0 1   0 0 0   1 1 1   0 0 1   1 0 0   0 1 1
		

Programs

  • Maple
    Compatible:= proc(i,j) local Xi,Xj,k;
    Xi:= Configs[i]; Xj:= Configs[j];
    if Xi[6..10] <> Xj[1..5] then return 0 fi;
    if Xi[1]=0 and ((Xi[6]=1 and Xj[6]=0) or (Xi[7]=1 and Xj[8]=0)) then return 0 fi;
    if Xi[2]=0 and ((Xi[7]=1 and Xj[7]=0) or (Xi[8]=1 and Xj[9]=0)) then return 0 fi;
    if Xi[3]=0 and ((Xi[7]=1 and Xj[6]=0) or (Xi[8]=1 and Xj[8]=0) or (Xi[9]=1 and Xj[10]=0)) then return 0 fi;
    if Xi[4]=0 and ((Xi[8]=1 and Xj[7]=0) or (Xi[9]=1 and Xj[9]=0)) then return 0 fi;
    if Xi[5]=0 and ((Xi[9]=1 and Xj[8]=0) or (Xi[10]=1 and Xj[10]=0)) then return 0 fi;
    1
    end proc:
    T:= Matrix(1024,1024,Compatible):
    u:= Vector(1024,1):
    Tu[0]:= u:
    for nn from 1 to 30 do Tu[nn]:= T . Tu[nn-1] od:
    32, seq(u^%T . Tu[n],n=0..30); # Robert Israel, Oct 22 2019

Formula

Linear recurrence of order 147 (see links). - Robert Israel, Oct 22 2019

A189621 Number of 6 X n binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

64, 4096, 61996, 515560, 6110500, 118571483, 2076231513, 28823835852, 385459961106, 5723963509791, 89346030665338, 1342965562065607, 19505273464622126, 285343732611331021, 4255443558501922341
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Row 6 of A189617.

Examples

			Some solutions for 6 X 3
..0..0..0....1..0..1....1..0..1....1..1..1....1..1..0....0..0..1....1..0..1
..1..0..1....0..1..1....1..0..0....1..0..0....1..1..1....1..0..1....1..1..1
..1..1..1....1..0..0....0..0..0....1..0..0....1..0..1....0..0..0....1..1..1
..0..1..1....0..0..1....1..0..0....1..1..1....1..1..0....0..0..1....1..1..0
..1..0..1....0..0..1....0..0..0....1..0..0....1..1..1....0..0..1....0..0..0
..1..1..0....1..0..1....1..1..1....1..0..1....1..1..0....0..0..1....1..0..1
		

Crossrefs

Cf. A189617.

A189622 Number of 7Xn binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

128, 16384, 371641, 4075336, 69943253, 2239578131, 61652076124, 1256763617551, 24523253340435, 553063756559791, 13299838117765230, 302455226663091586, 6562256770141965765, 144156209612197100001, 3257064388881887530527
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Row 7 of A189617

Examples

			Some solutions for 7X3
..0..0..1....0..0..0....0..0..1....0..0..0....0..0..1....0..0..1....0..0..1
..1..1..1....0..0..1....1..1..0....1..0..1....1..0..0....1..0..1....1..1..1
..1..0..1....0..0..1....1..1..1....1..1..1....1..0..0....1..0..1....1..1..1
..1..0..1....1..0..1....1..0..1....0..1..1....1..1..1....1..0..1....1..1..0
..1..1..1....1..1..0....1..0..1....0..1..1....1..1..1....0..0..0....0..0..0
..0..1..1....0..0..0....0..0..1....1..0..1....0..1..1....0..0..0....0..0..1
..1..1..0....1..0..1....1..0..1....1..1..1....1..0..0....1..1..0....1..1..1
		
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