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 1-7 of 7 results.

A188689 Number of nX3 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

7, 49, 218, 857, 3609, 15942, 69852, 302053, 1305379, 5658937, 24549216, 106431608, 461300682, 1999592300, 8668312567, 37577096221, 162893110032, 706125302623, 3060997024742, 13269191906269, 57520894059888, 249348416142040
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 3 of A188695

Examples

			Some solutions for 4X3
..0..1..1....1..0..1....1..1..0....1..0..1....1..0..0....1..0..0....0..0..1
..0..0..1....1..1..1....1..0..1....1..0..0....1..0..1....1..0..0....1..0..1
..0..0..1....1..1..1....0..1..1....0..0..0....1..0..1....1..0..0....1..0..1
..1..0..1....0..0..0....1..1..1....1..0..0....1..0..0....0..1..1....0..0..0
		

Formula

Empirical: a(n) = 5*a(n-1) -8*a(n-2) +21*a(n-3) +9*a(n-4) -23*a(n-5) +45*a(n-6) -57*a(n-7) -112*a(n-8) +55*a(n-9) +93*a(n-10) -3*a(n-11) -27*a(n-12) -4*a(n-13) -6*a(n-14)

A188690 Number of nX4 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

12, 144, 857, 4008, 20662, 120839, 708519, 3984317, 22096751, 123685638, 697749740, 3933600940, 22113174257, 124226310961, 698384857435, 3928070328882, 22091307667400, 124217141507585, 698440667872786
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 4 of A188695

Examples

			Some solutions for 5X4
..1..1..0..0....0..0..0..1....1..1..1..1....1..1..1..0....0..0..1..1
..1..0..0..0....1..0..0..1....0..0..0..1....1..1..1..0....0..0..1..1
..1..1..0..0....1..1..0..1....0..0..0..0....1..1..1..1....1..0..0..1
..1..1..0..0....1..1..0..0....1..0..0..0....1..1..0..1....1..1..0..1
..1..0..0..1....1..0..0..0....1..1..1..0....1..1..1..0....1..1..0..0
		

Formula

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +38*a(n-3) +44*a(n-4) -252*a(n-5) -94*a(n-6) -173*a(n-7) +417*a(n-8) +2548*a(n-9) -384*a(n-10) +1193*a(n-11) -4772*a(n-12) -6984*a(n-13) +6677*a(n-14) -10923*a(n-15) +16477*a(n-16) +4376*a(n-17) -6808*a(n-18) +1546*a(n-19) -4577*a(n-20) +1179*a(n-21) +3261*a(n-22) -1466*a(n-23) -63*a(n-24) +121*a(n-25) -246*a(n-26) +361*a(n-27) -334*a(n-28) -3*a(n-29) +149*a(n-30) -66*a(n-31) +4*a(n-32) +2*a(n-33)

A188691 Number of nX5 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

21, 441, 3609, 20662, 139307, 1181340, 9908740, 75877068, 567455273, 4366586742, 34248998327, 267095931282, 2063862354490, 15938318691269, 123521439902876, 958572046267137, 7431458286122944, 57564941872885645, 445967087965474764
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 5 of A188695

Examples

			Some solutions for 4X5
..0..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..1....1..1..0..0..0....0..1..1..1..1....0..0..0..0..0
..1..0..1..1..0....0..0..1..1..0....1..0..1..1..1....0..0..0..0..0
..1..0..1..1..1....1..1..1..1..1....1..0..0..1..1....1..1..1..0..1
		

Formula

Empirical: a(n) = 13*a(n-1) -72*a(n-2) +332*a(n-3) -521*a(n-4) -1967*a(n-5) +10379*a(n-6) -51424*a(n-7) +28054*a(n-8) +403549*a(n-9) -658172*a(n-10) +1849700*a(n-11) -1239067*a(n-12) -15670223*a(n-13) +24330475*a(n-14) -59850183*a(n-15) +88697426*a(n-16) +187045000*a(n-17) -330206715*a(n-18) +997106301*a(n-19) -2085486741*a(n-20) +905028643*a(n-21) -1558095425*a(n-22) -2656363440*a(n-23) +11436708343*a(n-24) -14013816831*a(n-25) +31212150218*a(n-26) -31183419729*a(n-27) +17494688482*a(n-28) -14737356475*a(n-29) -35106747755*a(n-30) +48351271081*a(n-31) -30134345302*a(n-32) +23300773627*a(n-33) +71424898322*a(n-34) -97405122786*a(n-35) +39818238895*a(n-36) +13587042357*a(n-37) -153008165143*a(n-38) +139402107983*a(n-39) +53993622733*a(n-40) -177575083625*a(n-41) +239479631120*a(n-42) -59992856699*a(n-43) -322136456306*a(n-44) +345822727924*a(n-45) -105090887373*a(n-46) -243206217394*a(n-47) +567737556458*a(n-48) -325846320221*a(n-49) -157377258816*a(n-50) +417062824086*a(n-51) -457382653146*a(n-52) +155724264358*a(n-53) +232274780565*a(n-54) -320874952433*a(n-55) +208706182428*a(n-56) -9426335629*a(n-57) -165554039782*a(n-58) +157631943987*a(n-59) -33193398897*a(n-60) -59171749202*a(n-61) +68583775952*a(n-62) -20708014940*a(n-63) -21735450662*a(n-64) +22924522215*a(n-65) -4140818762*a(n-66) -6471757632*a(n-67) +5315187407*a(n-68) -592210350*a(n-69) -1488577678*a(n-70) +830674024*a(n-71) -53562020*a(n-72) -111816478*a(n-73) +91187850*a(n-74) -31175524*a(n-75) -2956816*a(n-76) +5481352*a(n-77) -2588040*a(n-78) +552592*a(n-79) +66736*a(n-80) -58928*a(n-81) +21712*a(n-82) -2752*a(n-83) +144*a(n-84) +32*a(n-85)

A188692 Number of nX6 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

37, 1369, 15942, 120839, 1181340, 15547072, 196218615, 2192313402, 24054473035, 276006561506, 3234462955790, 37449962388209, 428641886155948, 4913977515021699, 56626336478764044, 653091347923944174
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 6 of A188695

Examples

			Some solutions for 4X6
..1..1..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..0....0..1..1..1..0..1
..0..0..0..0..0..1....1..1..0..1..1..1....1..1..1..1..1..0....0..1..1..1..0..1
..0..1..1..0..0..1....0..0..0..1..1..0....1..1..1..1..0..1....1..0..1..1..0..0
..1..1..1..1..0..0....1..0..0..1..1..1....0..0..1..1..0..1....1..1..1..1..1..0
		

A188693 Number of nX7 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

65, 4225, 69852, 708519, 9908740, 196218615, 3647921173, 58576420100, 923989193674, 15401563228402, 262861087544592, 4415950575544932, 73179716713561551, 1215743329351151607, 20324632650740759847
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 7 of A188695

Examples

			Some solutions for 4X7
..0..0..0..1..1..1..1....0..0..1..1..1..1..1....0..0..1..1..1..1..0
..0..0..1..1..1..1..0....0..0..0..0..1..1..1....0..0..0..0..0..1..1
..0..0..1..1..1..0..0....1..0..0..0..1..1..1....1..1..1..0..1..1..1
..0..0..1..1..1..0..0....1..1..1..1..1..1..1....1..1..1..1..1..1..1
		

A188694 Number of nX8 binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

114, 12996, 302053, 3984317, 75877068, 2192313402, 58576420100, 1302269111985, 28206984293659, 655766390218062, 15755573245806302, 370650107059787034, 8548930540422322425, 197761650191226073279, 4617841834907852976248
Offset: 1

Views

Author

R. H. Hardin Apr 08 2011

Keywords

Comments

Column 8 of A188695

Examples

			Some solutions for 4X8
..0..1..1..1..1..1..1..0....0..0..0..0..1..1..1..0....0..0..0..0..0..0..1..1
..0..0..1..1..0..0..0..0....0..0..0..1..1..1..1..0....0..0..0..1..1..1..0..0
..0..0..0..0..0..0..0..0....0..0..0..1..1..1..1..0....0..0..1..1..1..1..1..0
..0..0..0..0..1..1..0..0....0..0..1..1..1..1..1..1....0..0..1..1..1..1..1..1
		

A188688 Number of n X n binary arrays without the pattern 0 1 0 diagonally, vertically, antidiagonally or horizontally.

Original entry on oeis.org

2, 16, 218, 4008, 139307, 15547072, 3647921173, 1302269111985, 832889881464413, 1248703703842553735, 4253189666054817624993
Offset: 1

Views

Author

R. H. Hardin, Apr 08 2011

Keywords

Comments

Diagonal of A188695.

Examples

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

Crossrefs

Cf. A188695.
Showing 1-7 of 7 results.