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 1-4 of 4 results.

A233217 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

1, 2, 3, 6, 23, 11, 23, 376, 452, 48, 99, 7222, 35446, 10313, 236, 452, 147019, 3054973, 3638416, 249062, 1248, 2136, 3054973, 268289572, 1340889772, 380283286, 6147803, 6896, 10313, 63927526, 23644611625, 496475792293, 591021089923, 39892988056
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Table starts
....1.........2.............6.................23.....................99
....3........23...........376...............7222.................147019
...11.......452.........35446............3054973..............268289572
...48.....10313.......3638416.........1340889772...........496475792293
..236....249062.....380283286.......591021089923........919538740854193
.1248...6147803...39892988056....260625046992322....1703198747507336644
.6896.152986472.4187991850726.114934898294104873.3154729081272072714436

Examples

			Some solutions for n=3 k=4
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1
..2..1..2..1....0..1..5..1....0..2..2..1....2..0..0..0....0..2..1..3
..2..0..2..2....1..5..1..0....4..0..1..0....0..1..3..5....2..0..0..2

Links

Crossrefs

Column 1 is A233162(n+1)
Row 1 is A233106

Formula

Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 35*a(n-1) -259*a(n-2) +225*a(n-3)
k=3: a(n) = 127*a(n-1) -2331*a(n-2) +2205*a(n-3)
k=4: a(n) = 491*a(n-1) -22099*a(n-2) +21609*a(n-3)
k=5: a(n) = 1975*a(n-1) -228357*a(n-2) +1804281*a(n-3) -4170978*a(n-4) +2593080*a(n-5)
k=6: [order 7]
k=7: [order 11]
Empirical for row n:
n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
n=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3) for n>4
n=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5) for n>7
n=4: [order 9] for n>12
n=5: [order 19] for n>23
n=6: [order 42] for n>47

A233239 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

1, 2, 3, 6, 19, 11, 23, 271, 313, 48, 99, 4504, 18744, 6046, 236, 452, 79201, 1212549, 1409129, 123352, 1248, 2136, 1419889, 79794804, 338046654, 107709266, 2565169, 6896, 10313, 25622596, 5267525102, 81477098771, 94601758339, 8259321811
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Table starts
.......1............2..................6.......................23
.......3...........19................271.....................4504
......11..........313..............18744..................1212549
......48.........6046............1409129................338046654
.....236.......123352..........107709266..............94601758339
....1248......2565169.........8259321811...........26484848685044
....6896.....53692063.......633724470764.........7415057313896849
...39168...1126297996.....48630297616989......2076029517168733114
..226496..23643610702...3731839458899046....581236325493128357679
.1325568.496455294319.286378755661153351.162731637919752077883024

Examples

			Some solutions for n=3 k=4
..0..1..0..2....0..0..1..2....0..1..0..2....0..0..1..0....0..0..1..2
..3..3..0..0....4..0..0..3....1..0..0..0....2..0..2..1....2..0..1..5
..0..3..3..4....3..0..4..2....2..2..0..2....2..1..2..2....1..5..3..5

Links

Crossrefs

Column 1 is A233162(n+1)
Column 2 is A233107
Row 1 is A233106

Formula

Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)
k=3: a(n) = 93*a(n-1) -1273*a(n-2) +1943*a(n-3) -882*a(n-4) +120*a(n-5)
k=4: a(n) = 311*a(n-1) -8722*a(n-2) +10022*a(n-3) -1645*a(n-4) +35*a(n-5)
Empirical for row n:
n=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
n=2: a(n) = 23*a(n-1) -81*a(n-2) -143*a(n-3) +82*a(n-4) +120*a(n-5) for n>6
n=3: [order 9] for n>10
n=4: [order 21] for n>22

A233147 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

1, 2, 2, 6, 16, 6, 23, 225, 225, 23, 99, 3727, 13259, 3727, 99, 452, 65120, 845917, 845917, 65120, 452, 2136, 1158334, 54777233, 198313130, 54777233, 1158334, 2136, 10313, 20726079, 3556749764, 46648134615, 46648134615, 3556749764, 20726079
Offset: 1

Views

Author

R. H. Hardin, Dec 04 2013

Keywords

Comments

Table starts
......1............2.................6......................23
......2...........16...............225....................3727
......6..........225.............13259..................845917
.....23.........3727............845917...............198313130
.....99........65120..........54777233.............46648134615
....452......1158334........3556749764..........10976545771938
...2136.....20726079......231058112982........2582927810338210
..10313....371568349....15011638934832......607799571521107132
..50469...6665506622...975308641633714...143023917159921251486
.249062.119595908140.63366149608139911.33655571006177475521033

Examples

			Some solutions for n=3 k=4
..0..0..0..1....0..0..0..0....0..0..0..1....0..0..1..1....0..0..0..1
..1..2..2..2....1..2..2..4....1..0..2..5....2..0..1..5....0..0..2..2
..2..1..2..4....5..5..2..4....3..4..5..5....1..2..2..2....3..1..0..2

Links

Crossrefs

Column 1 is A233106

Formula

Empirical for column k:
k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
k=2: a(n) = 25*a(n-1) -134*a(n-2) +134*a(n-3) -25*a(n-4) +a(n-5)
k=3: [order 10] for n>11
k=4: [order 27] for n>28

A233230 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Original entry on oeis.org

1, 2, 2, 6, 14, 6, 23, 174, 174, 23, 99, 2541, 8231, 2541, 99, 452, 39203, 420948, 420948, 39203, 452, 2136, 616454, 21895530, 72049266, 21895530, 616454, 2136, 10313, 9757236, 1142726121, 12389989684, 12389989684, 1142726121, 9757236, 10313
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2013

Keywords

Comments

Table starts
......1...........2................6.....................23
......2..........14..............174...................2541
......6.........174.............8231.................420948
.....23........2541...........420948...............72049266
.....99.......39203.........21895530............12389989684
....452......616454.......1142726121..........2131764323784
...2136.....9757236......59679029456........366805442634477
..10313...154782591....3117164734533......63115455429961173
..50469..2457231917..162820623245643...10860156414181066717
.249062.39019481264.8504746957840386.1868686679256045815893

Examples

			Some solutions for n=3 k=4
..0..1..1..1....0..1..2..1....0..1..1..2....0..1..0..0....0..1..2..1
..1..0..2..5....3..0..1..1....1..0..2..2....1..0..2..4....0..0..2..2
..1..0..1..1....3..0..2..5....1..1..1..1....1..2..4..5....0..1..1..0

Links

Crossrefs

Column 1 is A233106

Formula

Empirical for column k:
k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)
k=2: a(n) = 21*a(n-1) -79*a(n-2) -41*a(n-3) +72*a(n-4) +28*a(n-5)
k=3: [order 10]
k=4: [order 23]
Showing 1-4 of 4 results.

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