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

A188748 Number of 3 X n binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

7, 49, 292, 1723, 10327, 61996, 371641, 2227333, 13350748, 80027347, 479695855, 2875358812, 17235289777, 103310698477, 619258487404, 3711920099323, 22249757087527, 133368089673676, 799426585401961, 4791872379016597
Offset: 1

Views

Author

R. H. Hardin, Apr 09 2011

Keywords

Comments

Row 3 of A188747.

Examples

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

Formula

Empirical: a(n) = 6*a(n-1) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6).
Empirical g.f.: x*(7 + 7*x + 12*x^2 - 8*x^3 - 36*x^4 - 12*x^5) / (1 - 6*x + 2*x^2 - 11*x^3 - 10*x^4 + 30*x^5 + 12*x^6). - Colin Barker, Feb 20 2018

A188741 Number of nX3 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

8, 64, 292, 1651, 9504, 52072, 289776, 1617326, 8992115, 50039730, 278556885, 1550225927, 8627663414, 48018101493, 267244802833, 1487352476813, 8277889631533, 46070713404315, 256407195751421, 1427038070447781
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 3 of A188747

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +9*a(n-2) +50*a(n-3) +55*a(n-4) +37*a(n-5) -108*a(n-6) -111*a(n-7) +89*a(n-8) +27*a(n-9) -28*a(n-10) -5*a(n-11) -48*a(n-12) -28*a(n-13) -17*a(n-14) -4*a(n-15) -a(n-16)

A188742 Number of nX4 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

16, 256, 1723, 17286, 176002, 1605680, 15398676, 148041805, 1404107414, 13398153644, 127892153741, 1218764127847, 11622887616476, 110848330389832, 1056953079327533, 10079078798340060, 96114455989370660, 916528036067337866
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 4 of A188747

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +33*a(n-2) +225*a(n-3) -143*a(n-4) -1642*a(n-5) -3987*a(n-6) +11756*a(n-7) -3429*a(n-8) -9954*a(n-9) -12602*a(n-10) -51648*a(n-11) +366983*a(n-12) -243624*a(n-13) +497214*a(n-14) -600651*a(n-15) -869301*a(n-16) +1075547*a(n-17) -1622615*a(n-18) +2080991*a(n-19) -1707023*a(n-20) +2030078*a(n-21) -413613*a(n-22) -765573*a(n-23) -219698*a(n-24) +426694*a(n-25) +424840*a(n-26) -234199*a(n-27) -217206*a(n-28) -17093*a(n-29) +91431*a(n-30) +8022*a(n-31) -12640*a(n-32) -5538*a(n-33) +2116*a(n-34) +760*a(n-35) -216*a(n-36) -16*a(n-37)

A188743 Number of nX5 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

32, 1024, 10327, 184411, 3283906, 50067824, 828466161, 13666030547, 221062541460, 3615827505717, 59094131400635, 963450629620601, 15731137751927915, 256815197782250586, 4191335618980407425
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 5 of A188747

Examples

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

A188744 Number of nX6 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

64, 4096, 61996, 1944586, 60714322, 1536573216, 43558358008, 1229158478968, 33715030639152, 940176798492406, 26184077081950792, 726505692803789842, 20205409790700030932, 561795999161298554570, 15612682504741076575246
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 6 of A188747

Examples

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

A188745 Number of n X 7 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

128, 16384, 371641, 20544154, 1127318294, 47325959200, 2307086087740, 111642244016936, 5198138560322655, 247778079713183493, 11784953664767609408, 557503350633218495686, 26469014360403565983659
Offset: 1

Views

Author

R. H. Hardin, Apr 09 2011

Keywords

Comments

Column 7 of A188747.

Examples

			Some solutions for 3 X 7
..0..0..0..0..1..0..1....0..0..0..0..0..1..0....0..0..0..0..0..1..0
..1..1..1..0..1..1..0....1..0..0..0..1..0..1....1..0..1..1..0..0..0
..1..1..1..0..0..0..0....0..0..1..0..0..0..0....1..0..1..0..0..0..0
		

Crossrefs

Cf. A188747.

A188746 Number of nX8 binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

256, 65536, 2227333, 217243096, 20939826298, 1458401558672, 122293738629021, 10143499802360135, 801618812875139251, 65318162143525733827, 5304356577782619235403, 427773556302789402791981
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Column 8 of A188747

Examples

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

A188749 Number of 4 X n binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

13, 169, 1651, 17286, 184411, 1944586, 20544154, 217243096, 2296414963, 24275369558, 256625412014, 2712870938389, 28678635692942, 303171638077403, 3204930092906176, 33880400190604953, 358161194075528039
Offset: 1

Views

Author

R. H. Hardin, Apr 09 2011

Keywords

Comments

Row 4 of A188747.

Examples

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

Crossrefs

Cf. A188747.

Formula

Empirical: a(n) = 11*a(n-1) +2*a(n-2) -27*a(n-3) -420*a(n-4) -568*a(n-5) +3095*a(n-6) +2148*a(n-7) -2947*a(n-8) -4914*a(n-9) -3147*a(n-10) +1801*a(n-11) +4012*a(n-12) +2286*a(n-13) -228*a(n-14) -396*a(n-15) -656*a(n-16) -288*a(n-17) +192*a(n-18).

A188750 Number of 5Xn binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

24, 576, 9504, 176002, 3283906, 60714322, 1127318294, 20939826298, 388867222760, 7222456829200, 134147557893368, 2491616383146400, 46278849344155436, 859576817744096818, 15965664732975667282, 296544220226026744002
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Row 5 of A188747

Examples

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

Formula

Empirical: a(n) = 23*a(n-1) -70*a(n-2) -296*a(n-3) +2160*a(n-4) -14475*a(n-5) +17757*a(n-6) -1140806*a(n-7) +3091958*a(n-8) +12909222*a(n-9) -21584968*a(n-10) +52956008*a(n-11) -238059780*a(n-12) -437747824*a(n-13) +383951904*a(n-14) +179875536*a(n-15) +5217136240*a(n-16) +2716595936*a(n-17) +8603806528*a(n-18) -9963475328*a(n-19) -47487929344*a(n-20) -70724703488*a(n-21) -66827979008*a(n-22) +90736826112*a(n-23) +204642169856*a(n-24) +311200557056*a(n-25) +128833723392*a(n-26) -350912552960*a(n-27) -222173790208*a(n-28) +23629496320*a(n-29) -7108034560*a(n-30) +68068900864*a(n-31) +34536947712*a(n-32) -23668457472*a(n-33)

A188751 Number of 6Xn binary arrays without the pattern 1 1 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

44, 1936, 52072, 1605680, 50067824, 1536573216, 47325959200, 1458401558672, 44920478350336, 1383729806664224, 42625318691202112, 1313038765458668928, 40447195582501099328, 1245947218943096747520, 38380504925120799720192
Offset: 1

Views

Author

R. H. Hardin Apr 09 2011

Keywords

Comments

Row 6 of A188747

Examples

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

Formula

Empirical: a(n) = 38*a(n-1) -124*a(n-2) -3140*a(n-3) +8096*a(n-4) -259716*a(n-5) +4687896*a(n-6) -20613384*a(n-7) +158611248*a(n-8) -152099872*a(n-9) -13890193664*a(n-10) +55525795136*a(n-11) +4284484192*a(n-12) +18954549312*a(n-13) +3859060452864*a(n-14) -18802857067520*a(n-15) +6618272780544*a(n-16) -129224888191232*a(n-17) -307268058830848*a(n-18) +2671879628283392*a(n-19) -585615778051072*a(n-20) +39201937249583104*a(n-21) -37346178411466752*a(n-22) -196181188224899072*a(n-23) -537282380088098816*a(n-24) -2622956973995761664*a(n-25) +8868569915155144704*a(n-26) +4794513849125715968*a(n-27) +70931224429358727168*a(n-28) -56307294252038979584*a(n-29) -539141458256081846272*a(n-30) -113026663059443810304*a(n-31) -1737055429706877370368*a(n-32) +7690330843187796770816*a(n-33) +17066206218717563715584*a(n-34) +925263814637023920128*a(n-35) -15016901284292099833856*a(n-36) -262768297742713124552704*a(n-37) -237735194459221570617344*a(n-38) +208065137218162341707776*a(n-39) +583957561140035585048576*a(n-40) +3933460473824662014394368*a(n-41) +2505249088068863926468608*a(n-42) -3712513659214321713938432*a(n-43) -6531598835134203451932672*a(n-44) -30139657382461385138503680*a(n-45) -20079613559888106236149760*a(n-46) +5519863579946158974304256*a(n-47) +37778342641740928904069120*a(n-48) +207263786160210170693550080*a(n-49) +123006895613856303321972736*a(n-50) -101082629303525802179035136*a(n-51) -185319427418157801355083776*a(n-52) -618032763288494987391533056*a(n-53) -327276405047842411712086016*a(n-54) +561289977541862694919864320*a(n-55) +525810807819272801717583872*a(n-56) +534368575529962805707931648*a(n-57) +190648877353749529065684992*a(n-58) -759582431787077877045919744*a(n-59) -499791238369510015211929600*a(n-60) +146555837298938649803489280*a(n-61) +128070779632773779041550336*a(n-62) +52215683618678965419376640*a(n-63) +32064120172628401157308416*a(n-64) +1865524416321017685737472*a(n-65) -905725910647102129569792*a(n-66) -76701561858484315619328*a(n-67)
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