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 1-3 of 3 results.

A189617 T(n,k)=Number of nXk binary arrays without the pattern 0 1 0 diagonally, antidiagonally or horizontally.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 12, 49, 64, 16, 21, 144, 292, 256, 32, 37, 441, 1164, 1723, 1024, 64, 65, 1369, 5238, 8496, 10327, 4096, 128, 114, 4225, 25046, 50024, 65160, 61996, 16384, 256, 200, 12996, 116100, 357323, 532565, 515560, 371641, 65536, 512, 351, 40000
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Table starts
....2.......4........7.........12..........21.............37...............65
....4......16.......49........144.........441...........1369.............4225
....8......64......292.......1164........5238..........25046...........116100
...16.....256.....1723.......8496.......50024.........357323..........2482591
...32....1024....10327......65160......532565........6204967.........68121839
...64....4096....61996.....515560.....6110500......118571483.......2076231513
..128...16384...371641....4075336....69943253.....2239578131......61652076124
..256...65536..2227333...32031600...783072552....41236726541....1785011303305
..512..262144.13350748..251533888..8759983583...764615054191...52081392909734
.1024.1048576.80027347.1976926440.98440457351.14279876468131.1531637258052071

Examples

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

Links

Crossrefs

Column 3 is A188748
Row 1 is A005251(n+3)
Row 2 is A188501

A189696 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 diagonally, vertically or antidiagonally.

Original entry on oeis.org

2, 4, 4, 8, 16, 7, 16, 64, 49, 12, 32, 256, 292, 144, 20, 64, 1024, 1723, 1298, 400, 33, 128, 4096, 10327, 11637, 5172, 1089, 54, 256, 16384, 61996, 107720, 65297, 20316, 2916, 88, 512, 65536, 371641, 997264, 862652, 370045, 77752, 7744, 143, 1024, 262144
Offset: 1

Views

Author

R. H. Hardin Apr 25 2011

Keywords

Comments

Table starts
...2.....4.......8........16..........32............64.............128
...4....16......64.......256........1024..........4096...........16384
...7....49.....292......1723.......10327.........61996..........371641
..12...144....1298.....11637......107720........997264.........9205575
..20...400....5172.....65297......862652......11451149.......151788273
..33..1089...20316....370045.....7174919.....140346362......2748122586
..54..2916...77752...1999150....55423132....1553640701.....43645304766
..88..7744..295720..10867960...437257670...17872674996....733660344149
.143.20449.1117080..58328512..3370409239..198287096355..11722251157012
.232.53824.4209924.313915268.26229648516.2240961706438.192737455311869

Examples

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

Links

Crossrefs

Column 1 is A000071(n+3)
Column 2 is A188516
Row 3 is A188748

A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 292, 256, 32, 22, 256, 948, 1723, 1024, 64, 29, 484, 2527, 6454, 10327, 4096, 128, 37, 841, 5913, 18980, 44693, 61996, 16384, 256, 46, 1369, 12577, 49561, 136289, 321163, 371641, 65536, 512, 56, 2116, 24821, 119150
Offset: 1

Views

Author

R. H. Hardin Mar 25 2013

Keywords

Comments

Table starts
....2.......4........7........11.........16..........22..........29..........37
....4......16.......49.......121........256.........484.........841........1369
....8......64......292.......948.......2527........5913.......12577.......24821
...16.....256.....1723......6454......18980.......49561......119150......267643
...32....1024....10327.....44693.....136289......364959......920106.....2218590
...64....4096....61996....321163....1023339.....2715255.....6789502....16634224
..128...16384...371641...2343189....8052573....21347949....51831694...124050234
..256...65536..2227333..17087771...64796052...176196273...418107416...962697852
..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454
.1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946

Examples

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

Links

Crossrefs

Column 1 is A000079
Column 2 is A000302
Column 3 is A188748
Row 1 is A000124
Row 2 is A086601

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) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6)
k=4: [order 23]
k=5: [order 93]
Empirical for row n:
n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
n=3: a(n) = polynomial of degree 6 for n>1
n=4: a(n) = polynomial of degree 8 for n>6
n=5: a(n) = polynomial of degree 10 for n>12
n=6: a(n) = polynomial of degree 12 for n>20
Showing 1-3 of 3 results.

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

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