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 13 results. Next

A189257 Number of n X n binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

2, 16, 280, 8900, 552752, 68635317, 17747766886, 9421503162646, 10606582683139102, 24593238398265693575, 121227430181311808878846, 1234571538047080619811567488, 26705899629138438568650919545084
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Diagonal of A189264

Examples

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

A189258 Number of n X 3 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

7, 49, 280, 1600, 8985, 50397, 282332, 1581428, 8857677, 49611209, 277868792, 1556321080, 8716833601, 48822302485, 273449899316, 1531571519964, 8578212427349, 48045897623297, 269101318957392, 1507215463960672
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2011

Keywords

Comments

Column 3 of A189264.

Examples

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

Crossrefs

Cf. A189264.

Formula

Empirical: a(n) = 6*a(n-1) -2*a(n-2) +a(n-4) -50*a(n-5) -6*a(n-6) +140*a(n-7) -56*a(n-8).
Empirical g.f.: x*(7 + 7*x + 18*x^3 - 62*x^4 - 12*x^5 + 132*x^6 - 56*x^7) / (1 - 6*x + 2*x^2 - x^4 + 50*x^5 + 6*x^6 - 140*x^7 + 56*x^8). - Colin Barker, May 01 2018

A189259 Number of nX4 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

12, 144, 1156, 8900, 65760, 481552, 3510380, 25556548, 185975588, 1353139492, 9844797788, 71624858188, 521097138012, 3791166287372, 27582062117196, 200669125155708, 1459937829727116, 10621556383444668, 77275523001250188
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 4 of A189264

Examples

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

Formula

Empirical: a(n) = 9*a(n-1) -9*a(n-2) -27*a(n-3) +62*a(n-4) -522*a(n-5) +730*a(n-6) +2202*a(n-7) -3620*a(n-8) +5768*a(n-9) -7920*a(n-10) -45696*a(n-11) +71680*a(n-12) +75424*a(n-13) -146112*a(n-14) +13984*a(n-15) +51072*a(n-16) -17024*a(n-17) for n>18

A189260 Number of nX5 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

20, 400, 4720, 52748, 552752, 5746968, 59399960, 613358776, 6329670680, 65317473848, 674005375088, 6955021798680, 71768481603464, 740576822228336, 7641997047772264, 78857656505309336, 813731203352806672
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 5 of A189264

Examples

			Some solutions for 5X3
..0..0..0....0..0..1....1..0..0....1..1..1....1..1..1....0..0..1....0..0..0
..1..1..1....1..1..0....1..1..0....0..1..1....0..1..1....1..1..1....1..1..1
..1..1..1....0..1..1....0..1..0....0..1..0....1..1..1....1..1..0....1..0..1
..1..1..1....1..1..0....0..1..0....0..1..0....0..1..1....0..0..0....1..1..1
..0..0..1....1..1..1....0..1..0....0..1..0....1..0..0....1..0..0....0..0..0
		

Formula

Empirical: a(n) = 14*a(n-1) -30*a(n-2) -99*a(n-3) +356*a(n-4) -2856*a(n-5) +8692*a(n-6) +17040*a(n-7) -65040*a(n-8) +142172*a(n-9) -523592*a(n-10) -577136*a(n-11) +4758096*a(n-12) -3418384*a(n-13) -5978816*a(n-14) +8825824*a(n-15) -10155968*a(n-16) +18636928*a(n-17) -17683840*a(n-18) +1152*a(n-19) +18846208*a(n-20) -16343040*a(n-21) +1361920*a(n-22) +2150400*a(n-23) for n>24

A189261 Number of nX6 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

33, 1089, 18960, 308266, 4628486, 68635317, 1010709182, 14861981162, 218354201468, 3207581304325, 47115298896367, 692052648696687, 10165129114423772, 149309006382444045, 2193102055504811375
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 6 of A189264

Examples

			Some solutions for 6X3
..1..0..0....1..1..0....1..0..0....0..1..1....0..0..1....0..0..1....1..0..1
..0..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....0..0..0
..1..0..1....1..1..0....1..1..0....1..1..1....0..1..0....0..0..0....1..0..0
..1..1..0....1..1..0....1..0..1....1..1..0....1..1..0....1..1..0....0..0..0
..0..1..0....0..1..0....0..0..1....0..0..0....0..0..0....1..1..0....0..0..0
..1..0..0....0..1..0....1..0..1....0..1..0....0..0..0....0..1..0....0..0..0
		

Formula

Empirical: a(n) = 22*a(n-1) -94*a(n-2) -284*a(n-3) +1733*a(n-4) -11352*a(n-5) +67835*a(n-6) +76752*a(n-7) -853449*a(n-8) +901976*a(n-9) -5740086*a(n-10) +13739028*a(n-11) +44197303*a(n-12) +124759854*a(n-13) -1024073157*a(n-14) -2525205604*a(n-15) +14327510563*a(n-16) +712547050*a(n-17) -47952956322*a(n-18) +31323634540*a(n-19) -35406686682*a(n-20) +88990999576*a(n-21) +188444788988*a(n-22) -331486365542*a(n-23) -11633051789*a(n-24) -703000156294*a(n-25) +1085177784618*a(n-26) +1458830130414*a(n-27) -1766461853158*a(n-28) -476544246624*a(n-29) -234644319566*a(n-30) -2144529292192*a(n-31) +5969478396944*a(n-32) +1184010556568*a(n-33) -8359720474800*a(n-34) +1973474480880*a(n-35) +3293959223808*a(n-36) -249942799712*a(n-37) -608152874432*a(n-38) -947744263232*a(n-39) +572978394752*a(n-40) +131230520064*a(n-41) -58568504448*a(n-42) -12940005888*a(n-43) -838978560*a(n-44) for n>47

A189262 Number of nX7 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

54, 2916, 74869, 1771206, 38600001, 830564651, 17747766886, 379055775099, 8092834825779, 172797606124166, 3689743969531917, 78791192655511218, 1682561197005661625, 35931167376074022171, 767318458960721287707
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 7 of A189264

Examples

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

A189263 Number of nX8 binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

88, 7744, 293495, 10113920, 319000548, 9918543104, 305860450896, 9421503162646, 290030885325044, 8927631449810010, 274794811549580572, 8458248128908576878, 260346492261595728516, 8013524717628350193612, 246658279999619171732736
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 8 of A189264

Examples

			Some solutions for 8X3
..0..0..0....0..0..0....0..1..0....0..1..0....0..1..1....0..0..1....0..0..1
..1..1..1....1..1..1....0..1..1....1..0..1....1..1..1....1..1..0....1..1..1
..1..1..1....1..1..1....0..1..0....0..1..0....0..1..1....0..0..1....1..1..1
..1..1..1....1..0..1....0..1..1....1..0..1....1..1..1....1..1..1....0..0..1
..0..0..1....1..1..1....0..1..1....0..1..0....0..0..1....0..0..1....1..1..1
..1..1..1....0..0..0....0..1..0....0..0..0....1..1..1....1..1..0....1..1..0
..0..1..0....1..1..0....0..1..0....0..1..0....1..1..0....0..1..0....0..1..1
..1..1..1....1..1..0....0..1..0....0..0..0....1..1..1....0..0..0....1..0..0
		

A189265 Number of 3Xn binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

8, 64, 280, 1156, 4720, 18960, 74869, 293495, 1143065, 4435997, 17166670, 66321486, 255904884, 986647975, 3801894402, 14644645685, 56395631397, 217139104510, 835947689845, 3217998048544, 12387073741629, 47679941911196
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Row 3 of A189264

Examples

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

Formula

Empirical: a(n) = 6*a(n-1) +4*a(n-2) -71*a(n-3) +33*a(n-4) +318*a(n-5) -222*a(n-6) -671*a(n-7) +384*a(n-8) +626*a(n-9) +97*a(n-10) -36*a(n-11) -926*a(n-12) -422*a(n-13) +858*a(n-14) +428*a(n-15) -119*a(n-16) -274*a(n-17) -183*a(n-18) +127*a(n-19) +86*a(n-20) -35*a(n-21) -11*a(n-22) +4*a(n-23) for n>26

A189266 Number of 4Xn binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

16, 256, 1600, 8900, 52748, 308266, 1771206, 10113920, 57346260, 324067185, 1825263206, 10263448463, 57624947058, 323275736469, 1812337219071, 10156258833298, 56897386342175, 318690256627687, 1784770177500610
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Row 4 of A189264

Examples

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

Formula

Empirical: a(n) = 11*a(n-1) +6*a(n-2) -429*a(n-3) +744*a(n-4) +6940*a(n-5) -18686*a(n-6) -61135*a(n-7) +207251*a(n-8) +327069*a(n-9) -1285900*a(n-10) -1191543*a(n-11) +4464818*a(n-12) +3913359*a(n-13) -5610599*a(n-14) -15152375*a(n-15) -22015726*a(n-16) +51874387*a(n-17) +131891733*a(n-18) -95315883*a(n-19) -330266130*a(n-20) -63023574*a(n-21) +443243696*a(n-22) +823954870*a(n-23) -133267990*a(n-24) -2058918881*a(n-25) -805435608*a(n-26) +2214440258*a(n-27) +2061126100*a(n-28) +444511787*a(n-29) -2601539618*a(n-30) -4541374860*a(n-31) +1183757928*a(n-32) +5614189500*a(n-33) +1968385910*a(n-34) -1723818322*a(n-35) -4220004784*a(n-36) -3239576374*a(n-37) +3117105263*a(n-38) +4489476491*a(n-39) +172198024*a(n-40) -2127052100*a(n-41) -2238121394*a(n-42) -397778993*a(n-43) +1805165961*a(n-44) +1127845510*a(n-45) -453587085*a(n-46) -678915170*a(n-47) -251699836*a(n-48) +179974985*a(n-49) +247503147*a(n-50) +6307175*a(n-51) -77834308*a(n-52) -19125037*a(n-53) -930336*a(n-54) +4105014*a(n-55) +9881021*a(n-56) +958304*a(n-57) -4161588*a(n-58) -754666*a(n-59) +987914*a(n-60) +200309*a(n-61) -155304*a(n-62) -28777*a(n-63) +16413*a(n-64) +2222*a(n-65) -1068*a(n-66) -72*a(n-67) +32*a(n-68) for n>72

A189267 Number of 5Xn binary arrays without the pattern 0 0 1 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

32, 1024, 8985, 65760, 552752, 4628486, 38600001, 319000548, 2623974434, 21494294205, 175584444126, 1431440887081, 11653470772713, 94780732526327, 770355802817299, 6258416803590102, 50827354221378320, 412701823824877427
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Row 5 of A189264

Examples

			Some solutions for 5X3
..1..1..1....1..1..1....0..1..1....1..1..1....1..1..1....1..0..1....1..1..0
..0..1..1....1..0..0....0..1..0....0..1..0....0..1..1....1..0..0....0..1..1
..1..1..0....0..1..0....0..1..1....0..1..0....0..1..0....0..1..1....1..1..0
..0..1..0....1..1..0....1..0..0....0..1..0....0..1..1....0..1..1....1..1..0
..0..1..1....0..0..0....1..1..0....0..1..1....0..1..0....1..0..1....1..1..0
		
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