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 1-9 of 9 results.

A186119 Number of (n+1)X(n+1) binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

0, 38, 262, 4254, 90054, 4056794, 264173146, 33067061342, 6424488086390
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Diagonal of A186128

Examples

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

A186120 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

0, 14, 18, 50, 74, 182, 298, 678, 1186, 2566, 4690, 9830, 18498, 38006, 72914, 147974, 287554, 579222, 1135282, 2276710, 4488226, 8978102, 17768850, 35496326, 70442882, 140631254, 279616498, 558094758, 1111168738, 2217823222, 4420075090
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2011

Keywords

Comments

Column 1 of A186128.

Examples

			Some solutions for 3 X 2:
..0..1....1..1....1..0....0..0....1..1....0..0....1..0....1..0....0..1....0..1
..0..0....0..0....1..1....1..1....0..0....0..0....0..0....1..0....0..1....1..1
..1..0....1..1....0..1....0..0....0..0....1..1....0..1....1..0....0..1....1..0
		

Crossrefs

Cf. A186128.

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 6*a(n-4) - 4*a(n-5) for n>6.
Empirical g.f.: 2*x^2*(7 - 12*x - 2*x^2 + 4*x^3 - 8*x^4) / ((1 - 2*x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 17 2018

A186121 Number of (n+1) X 3 binary arrays with every 2 X 2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2 X 2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

14, 38, 94, 254, 682, 1878, 5214, 14606, 41138, 116350, 330046, 938174, 2670826, 7611430, 21707790, 61943694, 176825074, 504902766, 1441965358, 4118707422, 11765461418, 33611411190, 96025298558, 274346613774, 783834214130
Offset: 1

Views

Author

R. H. Hardin, Feb 13 2011

Keywords

Comments

Column 2 of A186128.

Examples

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

Crossrefs

Cf. A186128.

Formula

Empirical: a(n) = 5*a(n-1) - 3*a(n-2) - 13*a(n-3) + 6*a(n-4) + 14*a(n-5) + 6*a(n-6) + 8*a(n-7) - 16*a(n-8) - 16*a(n-9).
Empirical g.f.: 2*x*(7 - 16*x - 27*x^2 + 40*x^3 + 52*x^4 + 14*x^5 - 4*x^6 - 72*x^7 - 64*x^8) / ((1 - 2*x)*(1 - 3*x - 3*x^2 + 7*x^3 + 8*x^4 + 2*x^5 - 2*x^6 - 12*x^7 - 8*x^8)). - Colin Barker, Apr 17 2018

A186122 Number of (n+1)X4 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

18, 94, 262, 946, 2978, 10502, 34678, 120290, 405274, 1395998, 4745006, 16291134, 55591062, 190569866, 651446994, 2231635906, 7634948674, 26146587758, 89488608966, 306421554338, 1048950425454, 3591569027638, 12295940315506
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 3 of A186128

Examples

			Some solutions for 3X4
..1..0..0..0....1..1..0..0....1..0..0..1....1..0..0..0....0..1..0..0
..1..0..0..0....1..1..1..1....0..0..0..0....1..0..0..0....0..0..0..1
..0..0..1..1....0..0..1..1....0..1..1..0....1..0..0..0....1..0..0..1
		

Formula

Empirical: a(n)=7*a(n-1)-a(n-2)-83*a(n-3)+105*a(n-4)+366*a(n-5)-566*a(n-6)-920*a(n-7)+1225*a(n-8)+1920*a(n-9)-1210*a(n-10)-3435*a(n-11)-521*a(n-12)+4429*a(n-13)+4158*a(n-14)-3945*a(n-15)-6055*a(n-16)+1059*a(n-17)+4227*a(n-18)+1217*a(n-19)-275*a(n-20)-965*a(n-21)-1160*a(n-22)-245*a(n-23)+357*a(n-24)+391*a(n-25)+5*a(n-26)-292*a(n-27)-120*a(n-28)+80*a(n-29)+80*a(n-30)+64*a(n-31) for n>33

A186123 Number of (n+1)X5 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

50, 254, 946, 4254, 17794, 79782, 350266, 1574348, 7039308, 31791832, 143422488, 649853710, 2944761666, 13369773598, 60719993934, 276010194872, 1254976548136, 5708622661652, 25972110429080, 118188673239130, 537890728864526
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 4 of A186128

Examples

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

Formula

Empirical: a(n)=13*a(n-1)-27*a(n-2)-313*a(n-3)+1360*a(n-4)+2960*a(n-5)-21942*a(n-6)-11823*a(n-7)+207082*a(n-8)-8597*a(n-9)-1365516*a(n-10)+273265*a(n-11)+6957547*a(n-12)-661483*a(n-13)-29271261*a(n-14)-5183365*a(n-15)+105123375*a(n-16)+53449823*a(n-17)-322792246*a(n-18)-264403445*a(n-19)+833623544*a(n-20)+917183114*a(n-21)-1771318700*a(n-22)-2500483447*a(n-23)+3014800837*a(n-24)+5679518352*a(n-25)-3928025864*a(n-26)-11068642898*a(n-27)+3449723643*a(n-28)+18652699704*a(n-29)-720507050*a(n-30)-27075919990*a(n-31)-4150074641*a(n-32)+33684461501*a(n-33)+9845557873*a(n-34)-36002318878*a(n-35)-14320175787*a(n-36)+33511328801*a(n-37)+15681313926*a(n-38)-27614165654*a(n-39)-13198975601*a(n-40)+20498342300*a(n-41)+7233225845*a(n-42)-14234922396*a(n-43)+1351829704*a(n-44)+9789428363*a(n-45)-10132487225*a(n-46)-7385233165*a(n-47)+15981020015*a(n-48)+7209995908*a(n-49)-17486996880*a(n-50)-9135579843*a(n-51)+14919288619*a(n-52)+11444925467*a(n-53)-9093755033*a(n-54)-11423688533*a(n-55)+2516202348*a(n-56)+8167361183*a(n-57)+1449757374*a(n-58)-3957191684*a(n-59)-2063583521*a(n-60)+1240084684*a(n-61)+1208640257*a(n-62)-212076992*a(n-63)-490905835*a(n-64)-65556295*a(n-65)+112985115*a(n-66)+117620104*a(n-67)+51984509*a(n-68)-76189430*a(n-69)-70949032*a(n-70)+39949387*a(n-71)+45626975*a(n-72)-17536162*a(n-73)-25550856*a(n-74)+4728478*a(n-75)+13766856*a(n-76)+2272908*a(n-77)-5218884*a(n-78)-2862290*a(n-79)+658554*a(n-80)+1147760*a(n-81)+206358*a(n-82)-177984*a(n-83)-90256*a(n-84)+4684*a(n-85)+11996*a(n-86)+200*a(n-87)-464*a(n-88)-96*a(n-89)+128*a(n-90) for n>92

A186124 Number of (n+1)X6 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

74, 682, 2978, 17794, 90054, 539962, 2915982, 17129792, 95854320, 556779864, 3165362160, 18297969958, 104743900094, 604164804194, 3469208600426, 19989944278608, 114949082280552, 662041931628544, 3809464845425408
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 5 of A186128

Examples

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

A186125 Number of (n+1)X7 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

182, 1878, 10502, 79782, 539962, 4056794, 29491822, 220010616, 1637583596, 12272724126, 92041463782, 692502277290, 5211824476838, 39292304082970, 296277012735686, 2235990214584584, 16877344601227160, 127445629177320202
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 6 of A186128

Examples

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

A186126 Number of (n+1)X8 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

298, 5214, 34678, 350266, 2915982, 29491822, 264173146, 2630528360, 24515504568, 241032804442, 2294311413454, 22390251063942, 215298723003602, 2093763781095758, 20224956581082238, 196384193909326548
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 7 of A186128

Examples

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

A186127 Number of (n+1)X9 binary arrays with every 2X2 subblock diagonal sum less antidiagonal sum equal to some horizontal or vertical neighbor 2X2 subblock diagonal sum less antidiagonal sum.

Original entry on oeis.org

678, 14606, 120290, 1574348, 17129792, 220010616, 2630528360, 33067061342, 411149162658, 5153688541776, 64828282889916, 815418585280038, 10288257115910818, 129785918260715398, 1639362506927114546
Offset: 1

Views

Author

R. H. Hardin Feb 13 2011

Keywords

Comments

Column 8 of A186128

Examples

			Some solutions for 3X9
..1..1..0..0..1..0..0..1..1....1..1..0..1..1..0..0..1..1
..1..1..1..0..0..0..1..1..1....0..0..0..1..1..1..0..0..0
..0..0..1..0..0..1..1..0..0....0..0..1..1..0..1..1..0..0
		
Showing 1-9 of 9 results.