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.

A283543 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

2, 4, 4, 7, 11, 8, 13, 27, 33, 16, 24, 76, 127, 98, 32, 44, 201, 578, 573, 291, 64, 81, 537, 2369, 4089, 2615, 865, 128, 149, 1444, 10069, 25532, 29558, 11903, 2570, 256, 274, 3859, 42664, 167920, 282773, 212441, 54211, 7637, 512, 504, 10339, 179733, 1094959
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2017

Keywords

Comments

Table starts
....2.....4.......7........13..........24............44..............81
....4....11......27........76.........201...........537............1444
....8....33.....127.......578........2369.........10069...........42664
...16....98.....573......4089.......25532........167920.........1094959
...32...291....2615.....29558......282773.......2905717........29377334
...64...865...11903....212441.....3109801......49760703.......778500603
..128..2570...54211...1529463....34266804.....854841910.....20707472573
..256..7637..246869..11006233...377393657...14672363665....550220030803
..512.22693.1124239..79212552..4156954825..251901309671..14624495679716
.1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840

Examples

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

Links

Crossrefs

Column 1 is A000079.
Column 2 is A282990.
Row 1 is A000073(n+3).
Row 2 is A282641.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)
k=4: [order 8]
k=5: [order 21]
k=6: [order 27]
k=7: [order 59]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3)
n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)
n=4: [order 8]
n=5: [order 21]
n=6: [order 32]
n=7: [order 69]

A297682 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 4 neighboring 1s.

Original entry on oeis.org

2, 4, 4, 7, 11, 8, 13, 29, 33, 16, 24, 80, 150, 98, 32, 44, 219, 629, 742, 291, 64, 81, 597, 2790, 4633, 3744, 865, 128, 149, 1632, 12110, 32911, 34872, 18840, 2570, 256, 274, 4459, 52889, 221420, 401678, 260924, 94891, 7637, 512, 504, 12181, 230406, 1519630
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2018

Keywords

Comments

Table starts
...2.....4.......7........13.........24...........44.............81
...4....11......29........80........219..........597...........1632
...8....33.....150.......629.......2790........12110..........52889
..16....98.....742......4633......32911.......221420........1519630
..32...291....3744.....34872.....401678......4202440.......45865837
..64...865...18840....260924....4870764.....78957968.....1368968852
.128..2570...94891...1955750...59210634...1487819051....41030621948
.256..7637..477850..14651847..719647644..28013761161..1229127412701
.512.22693.2406649.109783269.8748946600.527589764007.36837288191422

Examples

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

Links

Crossrefs

Column 1 is A000079.
Column 2 is A282990.
Row 1 is A000073(n+3).
Row 2 is A124861(n+1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
k=3: a(n) = 5*a(n-1) -a(n-2) +8*a(n-3) -5*a(n-4) -30*a(n-5) +17*a(n-6)
k=4: [order 16]
k=5: [order 30]
k=6: [order 57]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +2*a(n-4)
n=3: [order 8]
n=4: [order 17]
n=5: [order 41]

A295275 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.

Original entry on oeis.org

2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 164, 98, 24, 44, 291, 811, 811, 291, 44, 81, 865, 4035, 6659, 4035, 865, 81, 149, 2570, 19997, 54773, 54773, 19997, 2570, 149, 274, 7637, 99245, 449827, 748740, 449827, 99245, 7637, 274, 504, 22693, 492401, 3697742
Offset: 1

Views

Author

R. H. Hardin, Nov 19 2017

Keywords

Comments

Table starts
...2.....4.......7........13..........24............44..............81
...4....11......33........98.........291...........865............2570
...7....33.....164.......811........4035.........19997...........99245
..13....98.....811......6659.......54773........449827.........3697742
..24...291....4035.....54773......748740......10203847.......139221499
..44...865...19997....449827....10203847.....230659662......5221177246
..81..2570...99245...3697742...139221499....5221177246....196091375073
.149..7637..492401..30386185..1898916677..118139247475...7361533108317
.274.22693.2443097.249719021.25902054180.2673342943199.276386201580189

Examples

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

Links

Crossrefs

Columns are A000073(n+3), A282990, A295270, A295271, A295272, A295273, A295274.
Diagonal is A295269.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
k=3: [order 10]
k=4: [order 16]
k=5: [order 40]
k=6: [order 78]

A282996 T(n,k) is the number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

Original entry on oeis.org

2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 163, 98, 24, 44, 291, 803, 803, 291, 44, 81, 865, 3971, 6547, 3971, 865, 81, 149, 2570, 19587, 53389, 53389, 19587, 2570, 149, 274, 7637, 96693, 435027, 720417, 435027, 96693, 7637, 274, 504, 22693, 477297, 3546870
Offset: 1

Views

Author

R. H. Hardin, Feb 26 2017

Keywords

Examples

			Table starts:
...2.....4........7.........13...........24.............44...............81
...4....11.......33.........98..........291............865.............2570
...7....33......163........803.........3971..........19587............96693
..13....98......803.......6547........53389.........435027..........3546870
..24...291.....3971......53389.......720417........9706901........130854309
..44...865....19587.....435027......9706901......216173426.......4817792042
..81..2570....96693....3546870....130854309.....4817792042.....177509416175
.149..7637...477297...28911809...1763845523...107354061547....6539125324144
.274.22693..2355925..235681253..23775564134..2392171690343..240894164469261
.504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833
Some solutions for n=5 and k=4:
..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1
..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0
..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0
..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0

Links

Crossrefs

Columns are A000073(n+3), A282990, A282991, A282992, A282993, A282994, A282995.
Diagonal is A067968.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3);
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4);
k=3: [order 9];
k=4: [order 15];
k=5: [order 36];
k=6: [order 69].
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.