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.

A207752 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 12, 81, 102, 81, 14, 16, 144, 289, 270, 196, 22, 20, 256, 612, 900, 798, 484, 35, 25, 400, 1296, 2100, 3249, 2354, 1225, 56, 30, 625, 2340, 4900, 8778, 11449, 7210, 3136, 90, 36, 900, 4225, 9450, 23716, 34668, 42436, 22232, 8100, 145, 42
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4.....6......9.....12......16......20.......25.......30........36
..4...16....36.....81....144.....256.....400......625......900......1296
..6...36...102....289....612....1296....2340.....4225.....6890.....11236
..9...81...270....900...2100....4900....9450....18225....31185.....53361
.14..196...798...3249...8778...23716...51590...112225...213060....404496
.22..484..2354..11449..34668..104976..247860...585225..1182690...2390116
.35.1225..7210..42436.147084..509796.1341606..3530641..7826035..17347225
.56.3136.22232.157609.617732.2421136.6978660.20115225.47881860.113976976

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Row 1 is A002620(n+2)
Row 2 is A030179(n+2)
Row 3 is A207118

A207403 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 12, 81, 102, 64, 10, 16, 144, 289, 216, 100, 12, 20, 256, 612, 729, 390, 144, 14, 25, 400, 1296, 1782, 1521, 636, 196, 16, 30, 625, 2340, 4356, 4212, 2809, 966, 256, 18, 36, 900, 4225, 8910, 11664, 8692, 4761, 1392, 324, 20, 42, 1296
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2...4....6....9....12.....16.....20.....25......30......36.......42.......49
..4..16...36...81...144....256....400....625.....900....1296.....1764.....2401
..6..36..102..289...612...1296...2340...4225....6890...11236....17066....25921
..8..64..216..729..1782...4356...8910..18225...33210...60516...101598...170569
.10.100..390.1521..4212..11664..26676..61009..123006..248004...456666...840889
.12.144..636.2809..8692..26896..68060.172225..380970..842724..1690038..3389281
.14.196..966.4761.16284..55696.154580.429025.1033590.2490084..5404650.11730625
.16.256.1392.7569.28362.106276.321110.970225.2529480.6594624.15405432.35988001

Examples

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

Links

Crossrefs

Column 2 is A016742
Column 3 is A086113
Row 1 is A002620(n+2)
Row 2 is A030179(n+2)
Row 3 is A207118

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
k=4: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1
k=5: a(n) = (1/3)*n^5 + 3*n^4 + (28/3)*n^3 + 7*n^2 - (29/3)*n + 2
k=6: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4
k=7: a(n) = (1/36)*n^7 + (4/9)*n^6 + (53/18)*n^5 + (91/9)*n^4 + (589/36)*n^3 + (31/9)*n^2 - (58/3)*n + 6

A207949 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 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, 12, 81, 102, 100, 16, 16, 144, 289, 370, 256, 26, 20, 256, 612, 1369, 1232, 676, 42, 25, 400, 1296, 3478, 5929, 4238, 1764, 68, 30, 625, 2340, 8836, 18172, 26569, 14406, 4624, 110, 36, 900, 4225, 18330, 55696, 98126, 117649
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6......9......12.......16.......20........25........30.........36
..4...16....36.....81.....144......256......400.......625.......900.......1296
..6...36...102....289.....612.....1296.....2340......4225......6890......11236
.10..100...370...1369....3478.....8836....18330.....38025.....69420.....126736
.16..256..1232...5929...18172....55696...133812....321489....662256....1364224
.26..676..4238..26569...98126...362404..1007146...2798929...6501278...15100996
.42.1764.14406.117649..524104..2334784..7513176..24176889..63380130..166152100
.68.4624.49164.522729.2806686.15069924.56114310.208947025.617864520.1827049536

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207249
Column 4 is A207854
Row 1 is A002620(n+2)
Row 2 is A030179(n+2)
Row 3 is A207118
Showing 1-3 of 3 results.

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