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.

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A207346 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 13, 81, 84, 100, 16, 18, 169, 192, 292, 256, 26, 25, 324, 426, 828, 912, 676, 42, 34, 625, 858, 2190, 3130, 2812, 1764, 68, 46, 1156, 1704, 5290, 9668, 11230, 8928, 4624, 110, 62, 2116, 3330, 12292, 27022, 41112, 43260, 28152
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2....4.....6......9.....13......18.......25.......34........46........62
..4...16....36.....81....169.....324......625.....1156......2116......3844
..6...36....84....192....426.....858.....1704.....3330......6390.....12150
.10..100...292....828...2190....5290....12292....27978.....62574....136978
.16..256...912...3130...9668...27022....71344...185624....468864...1161400
.26..676..2812..11230..41112..128292...388134..1134282...3225374...9002616
.42.1764..8928..43260.186002..684324..2367656..8000806..26057006..82907430
.68.4624.28152.163710.828530.3524736.13950908.53882188.199473062.720751822

Examples

			Some solutions for n=4 k=3
..0..0..1....0..1..0....0..0..1....1..1..1....1..1..1....1..1..1....1..1..0
..0..0..1....0..0..1....1..1..1....1..1..0....0..0..1....1..1..0....1..1..1
..1..1..0....1..1..0....1..0..0....0..0..1....0..1..0....0..0..1....0..0..1
..1..1..0....1..0..0....0..0..1....1..1..0....1..0..0....0..1..0....1..1..0

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 1 is A171861(n+1)
Row 2 is A207025

A207589 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 60, 81, 13, 26, 256, 144, 144, 169, 18, 42, 676, 324, 432, 312, 324, 25, 68, 1764, 756, 1098, 1014, 612, 625, 34, 110, 4624, 1728, 3150, 3094, 2232, 1250, 1156, 46, 178, 12100, 3996, 8244, 9698, 7272, 5000, 2516, 2116, 62
Offset: 1

Views

Author

R. H. Hardin, Feb 19 2012

Keywords

Comments

Table starts
..2....4....6....10....16.....26.....42......68......110......178.......288
..4...16...36...100...256....676...1764....4624....12100....31684.....82944
..6...36...60...144...324....756...1728....3996.....9180....21168.....48708
..9...81..144...432..1098...3150...8244...23202....61560...171468....458640
.13..169..312..1014..3094...9698..30056...93782...291304...908102...2822456
.18..324..612..2232..7272..25776..85536..300096..1004364..3501756..11782620
.25..625.1250..5000.18150..70800.263550.1018700..3824100.14714500..55475900
.34.1156.2516.11220.46716.204476.876860.3832616.16578128.72435844.314466680

Examples

			Some solutions for n=4, k=3
..0..1..1....1..0..0....1..0..1....1..1..1....1..0..1....0..1..0....1..0..0
..1..0..1....0..1..1....0..1..1....0..1..0....0..1..0....1..0..0....1..1..1
..0..1..0....1..1..0....1..0..0....1..0..0....1..0..1....0..1..0....0..1..1
..1..1..1....1..0..0....1..0..1....0..1..0....1..1..0....1..0..0....1..0..0

Links

Crossrefs

Column 1 is A171861(n+1).
Column 2 is A207025.
Row 1 is A006355(n+2).
Row 2 is A206981.

A207717 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 114, 81, 14, 26, 256, 450, 387, 196, 22, 42, 676, 1644, 2205, 1414, 484, 35, 68, 1764, 6186, 12015, 11970, 5302, 1225, 56, 110, 4624, 23010, 66339, 97580, 66946, 20265, 3136, 90, 178, 12100, 85992, 364869, 805154
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4.....6......10.......16.........26..........42............68
..4...16....36.....100......256........676........1764..........4624
..6...36...114.....450.....1644.......6186.......23010.........85992
..9...81...387....2205....12015......66339......364869.......2009223
.14..196..1414...11970....97580.....805154.....6614706......54438356
.22..484..5302...66946...820820...10150118...125165018....1545006848
.35.1225.20265..383845..7070805..131365535..2433018665...45118588165
.56.3136.78120.2221688.61530000.1717508184.47808913432.1332236625328

Examples

			Some solutions for n=4 k=3
..1..1..1....1..1..1....1..0..1....0..1..0....1..0..0....1..0..1....1..0..1
..1..1..1....0..1..1....1..1..1....0..1..1....0..1..1....0..1..1....0..1..0
..1..1..1....1..1..1....0..1..0....0..1..1....1..1..0....1..0..0....1..1..1
..1..1..0....0..1..1....1..0..1....0..1..0....1..1..1....1..1..1....1..1..1

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A006355(n+2)
Row 2 is A206981

A207845 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 10, 16, 100, 72, 100, 16, 26, 256, 180, 240, 256, 26, 42, 676, 432, 780, 704, 676, 42, 68, 1764, 1044, 2320, 2816, 2080, 1764, 68, 110, 4624, 2520, 7140, 10144, 9672, 6216, 4624, 110, 178, 12100, 6084, 21600, 38208, 41444, 35952
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6.....10.....16......26.......42........68........110.........178
..4...16....36....100....256.....676.....1764......4624......12100.......31684
..6...36....72....180....432....1044.....2520......6084......14688.......35460
.10..100...240....780...2320....7140....21600.....65980.....200400......610740
.16..256...704...2816..10144...38208...140032....524480....1928000.....7206080
.26..676..2080...9672..41444..181896...794768...3479268...15223104....66632488
.42.1764..6216..35952.185136.1006572..5346600..28935984..154692048...835671396
.68.4624.18496.130152.813824.5427216.35345040.235865752.1547212432.10330674512

Examples

			Some solutions for n=4 k=3
..1..0..0....1..1..1....1..1..1....1..0..1....1..0..1....1..1..1....1..0..1
..0..1..1....1..0..1....1..0..1....0..1..0....1..0..1....1..0..1....1..0..0
..0..1..0....0..1..0....0..1..0....1..0..0....0..1..0....0..1..0....0..1..1
..1..0..1....0..1..1....1..1..1....0..1..1....1..0..0....0..1..0....0..1..0

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 1 is A006355(n+2)
Row 2 is A206981

A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal.

Original entry on oeis.org

1, 2, 1, 4, 6, 1, 6, 18, 16, 1, 10, 32, 74, 42, 1, 16, 82, 154, 308, 110, 1, 26, 162, 628, 734, 1282, 288, 1, 42, 388, 1470, 4906, 3472, 5338, 754, 1, 68, 806, 5530, 13170, 38986, 16338, 22228, 1974, 1, 110, 1858, 13906, 82526, 117690, 312276, 76630, 92562, 5168
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2013

Keywords

Comments

Table starts
.1.....2.......4.......6.........10.........16............26............42
.1.....6......18......32.........82........162...........388...........806
.1....16......74.....154........628.......1470..........5530.........13906
.1....42.....308.....734.......4906......13170.........82526........239992
.1...110....1282....3472......38986.....117690.......1274656.......4158066
.1...288....5338...16338.....312276....1047700......20052758......71916112
.1...754...22228...76630....2510674....9298730.....318521414....1241196022
.1..1974...92562..358656...20221026...82332898....5084744564...21383016966
.1..5168..385450.1676330..162993780..727588212...81376107850..367791626696
.1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234

Examples

			Some solutions for n=5 k=4
..2..1..0..1....2..1..2..1....2..1..0..2....1..2..0..2....2..1..0..1
..0..1..2..0....0..1..2..0....0..2..1..0....0..1..0..1....2..1..2..1
..2..0..1..0....2..0..1..0....1..2..1..0....2..1..2..1....2..1..0..2
..1..2..1..2....1..2..1..2....1..2..1..0....0..1..0..2....0..2..1..2
..1..0..1..0....1..2..1..0....1..0..2..1....2..1..0..2....1..0..1..2

Links

Crossrefs

Column 2 is A025169(n-1)
Column 3 is A218059
Row 1 is A006355(n+1)

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)
k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)
k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5
k=6: [order 7] for n>9
k=7: [order 16] for n>18
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) for n>3
n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6
n=3: [order 8] for n>12
n=4: [order 21] for n>24
n=5: [order 36] for n>42
n=6: [order 80] for n>87

A207254 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 8, 36, 36, 10, 10, 64, 102, 100, 16, 12, 100, 216, 370, 256, 26, 14, 144, 390, 940, 1232, 676, 42, 16, 196, 636, 1950, 3776, 4238, 1764, 68, 18, 256, 966, 3560, 9072, 15652, 14406, 4624, 110, 20, 324, 1392, 5950, 18688, 43498, 64176, 49164
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Table starts
..2....4.....6......8.....10......12......14.......16.......18.......20
..4...16....36.....64....100.....144.....196......256......324......400
..6...36...102....216....390.....636.....966.....1392.....1926.....2580
.10..100...370....940...1950....3560....5950.....9320....13890....19900
.16..256..1232...3776...9072...18688...34608....59264....95568...146944
.26..676..4238..15652..43498..101036..207298...388232...677898..1119716
.42.1764.14406..64176.206514..541380.1231650..2524704..4777290..8483748
.68.4624.49164.263976.982940.2906592.7328836.16436824.33693660.64313720

Examples

			Some solutions for n=4 k=3
..1..1..0....0..0..0....1..0..0....0..0..0....1..1..1....1..0..0....1..1..1
..1..0..0....0..0..0....0..0..0....0..1..1....1..1..1....1..0..0....1..1..1
..1..0..0....1..1..1....0..0..0....1..1..1....0..1..0....1..0..0....1..1..1
..0..1..1....1..1..1....0..1..1....1..0..0....0..1..0....1..0..0....1..1..1

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 2 is A016742
Row 3 is A086113

Formula

Empirical for row n:
n=1: a(k) = 2*k
n=2: a(k) = 4*k^2
n=3: a(k) = 2*k^3 + 6*k^2 - 2*k
n=4: a(k) = (5/6)*k^4 + (35/3)*k^3 - (5/6)*k^2 - (5/3)*k
n=5: a(k) = (4/15)*k^5 + (32/3)*k^4 + (44/3)*k^3 - (32/3)*k^2 + (16/15)*k
n=6: a(k) = (13/180)*k^6 + (143/20)*k^5 + (1235/36)*k^4 - (39/4)*k^3 - (377/45)*k^2 + (13/5)*k
n=7: a(k) = (1/60)*k^7 + (77/20)*k^6 + (2527/60)*k^5 + (119/4)*k^4 - (644/15)*k^3 + (42/5)*k^2 + (4/5)*k

A207453 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 90, 64, 10, 26, 256, 330, 168, 100, 12, 42, 676, 1008, 760, 270, 144, 14, 68, 1764, 3354, 2560, 1450, 396, 196, 16, 110, 4624, 10710, 10088, 5200, 2460, 546, 256, 18, 178, 12100, 34884, 36456, 23530, 9216, 3850, 720
Offset: 1

Views

Author

R. H. Hardin, Feb 17 2012

Keywords

Comments

Table starts
..2...4...6...10....16.....26.....42......68......110......178.......288
..4..16..36..100...256....676...1764....4624....12100....31684.....82944
..6..36..90..330..1008...3354..10710...34884...112530...364722...1179360
..8..64.168..760..2560..10088..36456..138176...509960..1910296...7096320
.10.100.270.1450..5200..23530..92610..396100..1610950..6754210..27799200
.12.144.396.2460..9216..46956.196812..932688..4086060.18819228..83939328
.14.196.546.3850.14896..84266.370734.1922564..8935850.44655394.212625504
.16.256.720.5680.22528.139984.640080.3599104.17556880.94358512.474439680

Examples

			Some solutions for n=5, k=3
..1..0..1....1..1..0....1..1..1....0..1..1....0..1..0....0..1..0....0..1..1
..1..0..1....1..0..0....0..1..1....0..1..1....0..1..1....1..0..0....1..0..1
..1..0..1....1..0..0....0..1..0....0..1..0....0..1..1....1..0..0....1..0..1
..1..0..1....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1
..1..0..0....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1

Links

Crossrefs

Column 2 is A016742.
Column 3 is A152746.
Row 1 is A006355(n+2).
Row 2 is A206981.

Formula

Empirical for column k:
k=1: a(n) = 2*n;
k=2: a(n) = 4*n^2;
k=3: a(n) = 12*n^2 - 6*n;
k=4: a(n) = 10*n^3 + 10*n^2 - 10*n;
k=5: a(n) = 48*n^3 - 32*n^2;
k=6: a(n) = 26*n^4 + 78*n^3 - 104*n^2 + 26*n;
k=7: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n;
k=8: a(n) = 68*n^5 + 408*n^4 - 612*n^3 + 204*n^2;
k=9: a(n) = 550*n^5 - 990*n^3 + 660*n^2 - 110*n;
k=10: a(n) = 178*n^6 + 1780*n^5 - 2670*n^4 + 534*n^3 + 534*n^2 - 178*n;
k=11: a(n) = 1728*n^6 + 1440*n^5 - 6912*n^4 + 5184*n^3 - 1152*n^2;
k=12: a(n) = 466*n^7 + 6990*n^6 - 9320*n^5 - 2796*n^4 + 8388*n^3 - 3728*n^2 + 466*n;
k=13: a(n) = 5278*n^7 + 10556*n^6 - 36946*n^5 + 27144*n^4 - 3016*n^3 - 3016*n^2 + 754*n;
k=14: a(n) = 1220*n^8 + 25620*n^7 - 25620*n^6 - 42700*n^5 + 73200*n^4 - 36600*n^3 + 6100*n^2;
k=15: a(n) = 15792*n^8 + 55272*n^7 - 165816*n^6 + 98700*n^5 + 39480*n^4 - 59220*n^3 + 19740*n^2 - 1974*n.
Empirical for row n:
n=1: a(k)=a(k-1)+a(k-2);
n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3);
n=3: a(k)=a(k-1)+7*a(k-2)+2*a(k-3)-4*a(k-4);
n=4: a(k)=a(k-1)+10*a(k-2)+3*a(k-3)-9*a(k-4);
n=5: a(k)=a(k-1)+13*a(k-2)+4*a(k-3)-16*a(k-4);
n=6: a(k)=a(k-1)+16*a(k-2)+5*a(k-3)-25*a(k-4);
n=7: a(k)=a(k-1)+19*a(k-2)+6*a(k-3)-36*a(k-4);
apparently for row n>2: a(k)=a(k-1)+(3*n-2)*a(k-2)+(n-1)*a(k-3)+(n-1)^2*a(k-4).

A207467 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 1 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 13, 81, 98, 100, 16, 18, 169, 271, 358, 256, 26, 25, 324, 677, 1307, 1152, 676, 42, 34, 625, 1504, 4219, 5369, 3910, 1764, 68, 46, 1156, 3399, 11760, 21517, 23645, 12994, 4624, 110, 62, 2116, 7220, 33393, 71928, 119965, 101233
Offset: 1

Views

Author

R. H. Hardin Feb 18 2012

Keywords

Comments

Table starts
..2....4.....6......9......13.......18........25........34.........46
..4...16....36.....81.....169......324.......625......1156.......2116
..6...36....98....271.....677.....1504......3399......7220......15184
.10..100...358...1307....4219....11760.....33393.....88198.....229458
.16..256..1152...5369...21517....71928....247631....778010....2406006
.26..676..3910..23645..119965...491948...2090927...7990970...29983194
.42.1764.12994.101233..644401..3205650..16675001..76629370..345252578
.68.4624.43596.439063.3523073.21396734.136803627.760840082.4139073950

Examples

			Some solutions for n=4 k=3
..0..1..0....1..1..0....0..0..1....1..1..1....0..1..0....0..0..1....0..0..1
..1..0..0....1..0..1....0..1..0....1..1..0....1..1..0....0..1..0....1..0..0
..1..0..1....1..0..1....0..1..0....1..0..0....1..1..1....1..1..0....1..1..0
..1..1..1....0..1..0....0..1..0....1..0..1....1..0..1....1..0..0....0..1..0

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A207112

A207661 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 84, 81, 14, 26, 256, 292, 198, 196, 22, 42, 676, 912, 870, 474, 484, 35, 68, 1764, 2812, 3358, 2774, 1140, 1225, 56, 110, 4624, 8928, 12040, 13902, 9060, 2748, 3136, 90, 178, 12100, 28152, 47320, 55752, 60762, 30440
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4....6.....10......16......26.......42.........68........110.........178
..4...16...36....100.....256.....676.....1764.......4624......12100.......31684
..6...36...84....292.....912....2812.....8928......28152......87972......277292
..9...81..198....870....3358...12040....47320.....182192.....676396.....2611234
.14..196..474...2774...13902...55752...284272....1391724....6009486....29516206
.22..484.1140...9060...60762..264568..1806676...11731102...56370696...366295198
.35.1225.2748..30440..284108.1296732.12327618..111194040..568720390..5097396968
.56.3136.6630.103838.1384420.6454684.87753008.1144562438.5955572036.76412972266

Examples

			Some solutions for n=4 k=3
..0..1..1....0..1..0....0..1..1....1..1..0....0..0..1....0..1..1....1..0..0
..1..0..0....1..1..0....1..0..0....1..0..1....1..1..0....1..1..0....0..1..1
..0..1..1....1..0..0....0..1..1....0..1..1....1..0..1....1..0..1....1..0..0
..1..1..0....0..1..0....1..0..1....1..1..0....1..1..0....0..1..1....0..1..1

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207341

A207928 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 15, 81, 72, 100, 16, 25, 225, 144, 240, 256, 26, 40, 625, 360, 576, 704, 676, 42, 64, 1600, 900, 1872, 1936, 2080, 1764, 68, 104, 4096, 2160, 6084, 7744, 6400, 6216, 4624, 110, 169, 10816, 5184, 18096, 30976, 29760, 21904
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....15......25.......40........64.......104........169
..4...16....36....81....225.....625.....1600......4096.....10816......28561
..6...36....72...144....360.....900.....2160......5184.....12528......30276
.10..100...240...576...1872....6084....18096.....53824....165648.....509796
.16..256...704..1936...7744...30976...111584....401956...1513992....5702544
.26..676..2080..6400..29760..138384...592968...2540836..11151624...48944016
.42.1764..6216.21904.126688..732736..3773248..19430464.105642128..574369156
.68.4624.18496.73984.520608.3663396.22906752.143233024.955190016.6369955344

Examples

			Some solutions for n=9 k=3
..0..0..1....0..0..1....0..1..1....1..0..0....1..0..0....0..0..1....0..0..1
..0..1..1....1..1..1....0..0..1....1..0..0....0..0..1....1..1..1....0..0..1
..1..1..0....1..0..0....1..0..0....0..1..1....1..1..0....1..1..0....1..1..0
..1..0..0....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..1..1
..0..1..1....1..1..0....1..1..1....1..1..0....0..0..1....1..0..1....1..0..0
..0..1..1....0..0..1....1..0..0....1..0..0....1..1..0....1..1..0....0..1..1
..1..0..0....1..0..0....0..1..1....0..1..1....0..1..1....0..1..1....1..0..1
..1..1..0....1..1..1....1..1..1....1..0..0....0..0..1....0..0..1....1..0..0
..0..1..1....0..1..1....1..0..0....1..1..1....1..0..0....1..1..0....0..1..1

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207840
Row 1 is A006498(n+2)
Row 2 is A189145(n+2)
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