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

A189189 Number of n X n binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

2, 16, 316, 15326, 1579664, 367115337, 184841938568, 209311662962608, 525679279319545840, 2979655033608039508606, 37875187935027408625277140, 1087648851912447148168100296827, 70353152136567154798416885107484140
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Diagonal of A189196

Examples

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

A189190 Number of nX3 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

8, 64, 316, 1494, 6446, 27170, 111778, 455376, 1841116, 7415070, 29785050, 119460218, 478648930, 1916674924, 7672027140, 30701884934, 122843150982, 491465083490, 1966100647058, 7865028551176, 31461745847388, 125851241881374
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Column 3 of A189196

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) -14*a(n-2) -29*a(n-3) +90*a(n-4) +12*a(n-5) -159*a(n-6) +36*a(n-7) +106*a(n-8) -35*a(n-9) -22*a(n-10) +8*a(n-11)

A189191 Number of nX4 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

16, 256, 2032, 15326, 101628, 657028, 4109278, 25421672, 155713446, 949556490, 5771152218, 35012940148, 212158079476, 1284620610228, 7774639010740, 47038657576938, 284540271729956, 1720987141305056, 10408196505797294
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Column 4 of A189196

Examples

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

Formula

Empirical: a(n) = 13*a(n-1) -24*a(n-2) -309*a(n-3) +1139*a(n-4) +2904*a(n-5) -15708*a(n-6) -13388*a(n-7) +114908*a(n-8) +27510*a(n-9) -517862*a(n-10) +10696*a(n-11) +1525375*a(n-12) -199987*a(n-13) -2999240*a(n-14) +537335*a(n-15) +3938119*a(n-16) -825688*a(n-17) -3403810*a(n-18) +826898*a(n-19) +1870596*a(n-20) -531896*a(n-21) -607828*a(n-22) +201144*a(n-23) +99904*a(n-24) -37536*a(n-25) -5568*a(n-26) +2304*a(n-27)

A189192 Number of nX5 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

32, 1024, 13045, 156564, 1579664, 15564047, 146936454, 1372985912, 12673978495, 116484051544, 1066397329392, 9744883834389, 88925544182556, 810852982213004, 7389628274064849, 67322696225968620, 613203444821642088
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Column 5 of A189196

Examples

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

Formula

Empirical: a(n) = 20*a(n-1) -26*a(n-2) -1758*a(n-3) +7884*a(n-4) +69274*a(n-5) -440875*a(n-6) -1621492*a(n-7) +13507948*a(n-8) +25172384*a(n-9) -274917184*a(n-10) -273994660*a(n-11) +4038604814*a(n-12) +2157309576*a(n-13) -44826838556*a(n-14) -12545085244*a(n-15) +386651971080*a(n-16) +55249249320*a(n-17) -2639477921890*a(n-18) -195034819700*a(n-19) +14437532484176*a(n-20) +622120688000*a(n-21) -63821395536740*a(n-22) -2013563540828*a(n-23) +229387235684075*a(n-24) +6204228280560*a(n-25) -673213717187734*a(n-26) -14708924451038*a(n-27) +1617830574782760*a(n-28) +18364193960110*a(n-29) -3187974181676823*a(n-30) +21749633597584*a(n-31) +5150273262854584*a(n-32) -172238338938872*a(n-33) -6807831142607116*a(n-34) +463812469077896*a(n-35) +7331518683699720*a(n-36) -804366669640684*a(n-37) -6387203643788164*a(n-38) +999955565998504*a(n-39) +4454231927925748*a(n-40) -921340393703952*a(n-41) -2449638785292204*a(n-42) +634177858926408*a(n-43) +1040892123443180*a(n-44) -324105066755064*a(n-45) -332359344974592*a(n-46) +120879015719960*a(n-47) +76775348266832*a(n-48) -31968235223312*a(n-49) -12165551078160*a(n-50) +5739648120864*a(n-51) +1221284783808*a(n-52) -653996805120*a(n-53) -67873787136*a(n-54) +42028015104*a(n-55) +1538030592*a(n-56) -1149603840*a(n-57)

A189193 Number of nX6 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

64, 4096, 83737, 1598444, 24496092, 367115337, 5218915180, 73539558380, 1021199649839, 14125557202206, 194506779840320, 2673686180231803, 36695207349332618, 503243079829310096, 6897499795974119793
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Column 6 of A189196

Examples

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

A189194 Number of nX7 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

128, 16384, 537496, 16316636, 379515360, 8646366042, 184841938568, 3925306136096, 81929775932500, 1704770564043390, 35287851485832028, 729339086587874460, 15048014087794649376, 310256937493956570170
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Column 7 of A189196

Examples

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

A189195 Number of n X 8 binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

256, 65536, 3450100, 166552852, 5878642448, 203562575017, 6541724250668, 209311662962608, 6564303642825447, 205436602739842458, 6391004867571530548, 198584429070400680915, 6158498206342385810146, 190869078020765592228428
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2011

Keywords

Comments

Column 8 of A189196.

Examples

			Some solutions for 3 X 8
..0..0..0..0..0..1..1..1....0..0..0..0..0..1..0..0....0..0..0..0..1..0..1..1
..1..1..1..1..0..1..1..1....1..1..1..1..1..1..1..1....0..1..1..1..0..1..1..1
..0..0..0..1..0..0..0..0....0..1..0..0..0..0..0..1....0..0..1..0..1..0..1..1
		

Crossrefs

Cf. A189196.

A189197 Number of 4 X n binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

12, 144, 1494, 15326, 156564, 1598444, 16316636, 166552852, 1700084336, 17353550112, 177135689224, 1808105575848, 18456166259888, 188390587782160, 1922989479244368, 19628839107258224, 200360599393734848
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2011

Keywords

Comments

Row 4 of A189196.

Examples

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

Crossrefs

Cf. A189196.

Formula

Empirical: a(n) = 12*a(n-1) -14*a(n-2) -52*a(n-3) +82*a(n-4) +16*a(n-5) -56*a(n-6) +16*a(n-7).
Empirical g.f.: 2*x*(1 - x)*(2 + 2*x - x^2)*(3 - 12*x^2 + 8*x^3) / (1 - 12*x + 14*x^2 + 52*x^3 - 82*x^4 - 16*x^5 + 56*x^6 - 16*x^7). - Colin Barker, May 01 2018

A189198 Number of 5Xn binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

20, 400, 6446, 101628, 1579664, 24496092, 379515360, 5878642448, 91053926856, 1410308064720, 21843768123936, 338330131913680, 5240270191277760, 81164599671831296, 1257128330483644640, 19471193573584406720
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Row 5 of A189196

Examples

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

Formula

Empirical: a(n) = 20*a(n-1) -60*a(n-2) -208*a(n-3) +844*a(n-4) +344*a(n-5) -3476*a(n-6) +3544*a(n-7) -1056*a(n-8)

A189199 Number of 6Xn binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

33, 1089, 27170, 657028, 15564047, 367115337, 8646366042, 203562575017, 4791913469442, 112799071668131, 2655202148877722, 62501206566986486, 1471224094156225703, 34631328118629702199, 815191106000869861143
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Row 6 of A189196

Examples

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

Formula

Empirical: a(n) = 33*a(n-1) -206*a(n-2) -738*a(n-3) +8753*a(n-4) -13693*a(n-5) -33068*a(n-6) +87427*a(n-7) -52757*a(n-8) +67082*a(n-9) -70312*a(n-10) -61118*a(n-11) +47608*a(n-12) -908*a(n-13) -1404*a(n-14) +568*a(n-15) -192*a(n-16)
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