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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A300804 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1672, 1672, 512, 32, 64, 2048, 12228, 23096, 12228, 2048, 64, 128, 8192, 89472, 317504, 317504, 89472, 8192, 128, 256, 32768, 654628, 4369224, 8170504, 4369224, 654628, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Mar 13 2018

Keywords

Comments

Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......228........1672.........12228............89472
...8....128.....1672.......23096........317504..........4369224
..16....512....12228......317504.......8170504........210678360
..32...2048....89472.....4369224.....210678360......10189867088
..64...8192...654628....60123512....5431609016.....492720806016
.128..32768..4789672...827349312..140040313680...23826737802264
.256.131072.35044228.11385017480.3610578476036.1152195114983576

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +3*a(n-2) -5*a(n-3)
k=4: [order 11]
k=5: [order 27] for n>29
k=6: [order 85] for n>87

A301407 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 252, 128, 16, 32, 512, 1988, 1988, 512, 32, 64, 2048, 15680, 31012, 15680, 2048, 64, 128, 8192, 123676, 483600, 483600, 123676, 8192, 128, 256, 32768, 975492, 7541492, 14905344, 7541492, 975492, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Mar 20 2018

Keywords

Comments

Table starts
...1......2........4...........8.............16...............32
...2......8.......32.........128............512.............2048
...4.....32......252........1988..........15680...........123676
...8....128.....1988.......31012.........483600..........7541492
..16....512....15680......483600.......14905344........459428416
..32...2048...123676.....7541492......459428416......27990353344
..64...8192...975492...117605364....14160945920....1705287652128
.128..32768..7694176..1833990416...436482419456..103893157740576
.256.131072.60687676.28600063044.13453684678656.6329599807409536

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +7*a(n-2)
k=4: a(n) = 13*a(n-1) +40*a(n-2) +9*a(n-3) -29*a(n-4) +4*a(n-5)
k=5: [order 8] for n>9
k=6: [order 22] for n>23
k=7: [order 45] for n>47

A301443 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 232, 128, 16, 32, 512, 1708, 1708, 512, 32, 64, 2048, 12576, 23672, 12576, 2048, 64, 128, 8192, 92616, 327848, 327848, 92616, 8192, 128, 256, 32768, 682084, 4543028, 8525992, 4543028, 682084, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Mar 21 2018

Keywords

Comments

Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......232........1708.........12576............92616
...8....128.....1708.......23672........327848..........4543028
..16....512....12576......327848.......8525992........221935656
..32...2048....92616.....4543028.....221935656......10857946336
..64...8192...682084....62956480....5777358820.....531234388944
.128..32768..5023328...872451104..150397035552...25991845818768
.256.131072.36995208.12090455460.3915165237488.1271713349901092

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1);
k=2: a(n) = 4*a(n-1);
k=3: a(n) = 8*a(n-1) -4*a(n-2) -5*a(n-3);
k=4: [order 11];
k=5: [order 31];
k=6: [order 97] for n>98.

A301784 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 240, 128, 16, 32, 512, 1808, 1808, 512, 32, 64, 2048, 13616, 25872, 13616, 2048, 64, 128, 8192, 102544, 369936, 369936, 102544, 8192, 128, 256, 32768, 772272, 5289488, 10033408, 5289488, 772272, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Mar 26 2018

Keywords

Comments

Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......240........1808.........13616...........102544
...8....128.....1808.......25872........369936..........5289488
..16....512....13616......369936......10033408........272151040
..32...2048...102544.....5289488.....272151040......14004742144
..64...8192...772272....75632400....7381982784.....720677122368
.128..32768..5816080..1081436176..200232929792...37085631944448
.256.131072.43801648.15463010576.5431228387584.1908405940870656

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +4*a(n-2)
k=4: a(n) = 13*a(n-1) +20*a(n-2) -16*a(n-3) -64*a(n-4)
k=5: [order 8]
k=6: [order 20]
k=7: [order 46]

A305523 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 219, 128, 16, 32, 512, 1482, 1482, 512, 32, 64, 2048, 10082, 16480, 10082, 2048, 64, 128, 8192, 68603, 186237, 186237, 68603, 8192, 128, 256, 32768, 466858, 2102155, 3536750, 2102155, 466858, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jun 04 2018

Keywords

Comments

Table starts
...1......2........4..........8...........16.............32................64
...2......8.......32........128..........512...........2048..............8192
...4.....32......219.......1482........10082..........68603............466858
...8....128.....1482......16480.......186237........2102155..........23747613
..16....512....10082.....186237......3536750.......66949063........1269418258
..32...2048....68603....2102155.....66949063.....2122076804.......67425576120
..64...8192...466858...23747613...1269418258....67425576120.....3592436519091
.128..32768..3177374..268359015..24080732454..2143769629842...191577652761963
.256.131072.21625010.3032800805.456869647792.68172646692968.10218588450186728

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1);
k=2: a(n) = 4*a(n-1);
k=3: a(n) = 6*a(n-1) +8*a(n-2) -10*a(n-3) -44*a(n-4) -30*a(n-5) for n>6;
k=4: [order 15] for n>17;
k=5: [order 58] for n>59;

A316808 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 247, 128, 16, 32, 512, 1905, 1905, 512, 32, 64, 2048, 14711, 28248, 14711, 2048, 64, 128, 8192, 113606, 420345, 420345, 113606, 8192, 128, 256, 32768, 877309, 6256258, 12075849, 6256258, 877309, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2018

Keywords

Comments

Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......247........1905.........14711...........113606
...8....128.....1905.......28248........420345..........6256258
..16....512....14711......420345......12075849........347046960
..32...2048...113606.....6256258.....347046960......19261290694
..64...8192...877309....93109949....9972851339....1068884675914
.128..32768..6774916..1385723098..286582122564...59316329979368
.256.131072.52318510.20623265507.8235306627639.3291689981719718

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -3*a(n-2) +7*a(n-3) -3*a(n-4)
k=4: a(n) = 15*a(n-1) -5*a(n-2) +50*a(n-3) -18*a(n-4) -81*a(n-5) +4*a(n-6) +20*a(n-7)
k=5: [order 22]
k=6: [order 59]

A316815 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 227, 128, 16, 32, 512, 1603, 1603, 512, 32, 64, 2048, 11339, 19816, 11339, 2048, 64, 128, 8192, 80196, 246196, 246196, 80196, 8192, 128, 256, 32768, 567185, 3056047, 5391628, 3056047, 567185, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jul 14 2018

Keywords

Comments

Table starts
...1......2........4..........8............16..............32................64
...2......8.......32........128...........512............2048..............8192
...4.....32......227.......1603.........11339...........80196............567185
...8....128.....1603......19816........246196.........3056047..........37935501
..16....512....11339.....246196.......5391628.......117897523........2578023456
..32...2048....80196....3056047.....117897523......4537910922......174669587289
..64...8192...567185...37935501....2578023456....174669587289....11834952392431
.128..32768..4011528..470942175...56382210217...6724877943937...802147875327622
.256.131072.28372197.5846244187.1233022160942.258886627124646.54360782611063950

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +10*a(n-2) -7*a(n-3) -64*a(n-4) -51*a(n-5) for n>6
k=4: [order 17] for n>18
k=5: [order 62] for n>63

A316960 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 220, 128, 16, 32, 512, 1498, 1498, 512, 32, 64, 2048, 10243, 16976, 10243, 2048, 64, 128, 8192, 70037, 194917, 194917, 70037, 8192, 128, 256, 32768, 478941, 2232443, 3796326, 2232443, 478941, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jul 17 2018

Keywords

Comments

Table starts
...1......2........4..........8...........16.............32................64
...2......8.......32........128..........512...........2048..............8192
...4.....32......220.......1498........10243..........70037............478941
...8....128.....1498......16976.......194917........2232443..........25592081
..16....512....10243.....194917......3796326.......73529753........1426910760
..32...2048....70037....2232443.....73529753.....2402722112.......78728223139
..64...8192...478941...25592081...1426910760....78728223139.....4359094468163
.128..32768..3275421..293396247..27687032205..2579211359302...241311689147759
.256.131072.22400407.3363774685.537290478883.84510945441118.13360998189431905

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 6*a(n-1) +9*a(n-2) -14*a(n-3) -52*a(n-4) -33*a(n-5) for n>6
k=4: [order 16] for n>17
k=5: [order 58] for n>59

A317517 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 255, 128, 16, 32, 512, 2032, 2032, 512, 32, 64, 2048, 16193, 32256, 16193, 2048, 64, 128, 8192, 129042, 512096, 512096, 129042, 8192, 128, 256, 32768, 1028335, 8130048, 16198017, 8130048, 1028335, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jul 30 2018

Keywords

Comments

Table starts
...1......2........4...........8.............16...............32
...2......8.......32.........128............512.............2048
...4.....32......255........2032..........16193...........129042
...8....128.....2032.......32256.........512096..........8130048
..16....512....16193......512096.......16198017........512358002
..32...2048...129042.....8130048......512358002......32289056648
..64...8192..1028335...129072576....16206294085....2034862700902
.128..32768..8194796..2049155072...512618027974..128237436273216
.256.131072.65304285.32532368768.16214518668763.8081548422775938

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -a(n-2) +6*a(n-3)
k=4: a(n) = 16*a(n-1) -6*a(n-2) +64*a(n-3)
k=5: [order 8]
k=6: [order 15]
k=7: [order 34]

A317525 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 248, 128, 16, 32, 512, 1921, 1921, 512, 32, 64, 2048, 14892, 28760, 14892, 2048, 64, 128, 8192, 115446, 431529, 431529, 115446, 8192, 128, 256, 32768, 894961, 6475106, 12547746, 6475106, 894961, 32768, 256, 512, 131072
Offset: 1

Views

Author

R. H. Hardin, Jul 30 2018

Keywords

Comments

Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......248........1921.........14892...........115446
...8....128.....1921.......28760........431529..........6475106
..16....512....14892......431529......12547746........364882328
..32...2048...115446.....6475106.....364882328......20564214798
..64...8192...894961....97158833...10610584063....1158965686460
.128..32768..6937925..1457871738..308552557709...65318143510572
.256.131072.53784248.21875422403.8972619323210.3681268128789010

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A004171(n-1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -2*a(n-2) +a(n-3) -3*a(n-4)
k=4: a(n) = 15*a(n-1) +a(n-2) -8*a(n-3) -84*a(n-4) -63*a(n-5) +24*a(n-6) +20*a(n-7)
k=5: [order 22]
k=6: [order 59]
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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