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.

A253326 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw.

Original entry on oeis.org

16, 44, 44, 121, 126, 121, 286, 373, 377, 286, 676, 1026, 1217, 848, 676, 1482, 2797, 3787, 2538, 2042, 1482, 3249, 6936, 11506, 7744, 6190, 4218, 3249, 6840, 17197, 31999, 23153, 19312, 11795, 9228, 6840, 14400, 39616, 86922, 66196, 58505, 34660
Offset: 1

Views

Author

R. H. Hardin, Dec 30 2014

Keywords

Comments

Table starts
....16....44....121....286.....676....1482....3249.....6840....14400.....29640
....44...126....373...1026....2797....6936...17197....39616....91571....200800
...121...377...1217...3787...11506...31999...86922...217799...537127...1242718
...286...848...2538...7744...23153...66196..185672...487946..1267072...3085862
...676..2042...6190..19312...58505..173903..503944..1397185..3802746...9816070
..1482..4218..11795..34660...98741..283804..797324..2204476..6007384..15848356
..3249..9228..25659..74953..210417..600020.1660088..4590122.12462900..33364770
..6840.18482..48085.132376..349857..952108.2516513..6753250.17839818..47266844
.14400.38621..99653.271506..705922.1887609.4869987.12802392.32941939..85796433
.29640.76654.188562.490768.1217364.3123964.7734273.19644544.48847302.123940122

Examples

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

Links

Crossrefs

Column 1 and row 1 are A204032

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
k=2: [order 13]
k=3: [same order 13] for n>15
k=4: [same order 13] for n>19
k=5: [same order 13] for n>22
k=6: [same order 13] for n>23
k=7: [same order 13] for n>26
Empirical for row n:
n=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
n=2: [order 21]
n=3: [order 39]
n=4: [order 45]
n=5: [order 63]
n=6: [order 65]
n=7: [order 87]

A235413 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing rowwise and nonincreasing columnwise.

Original entry on oeis.org

16, 44, 44, 121, 172, 121, 286, 704, 704, 286, 676, 2302, 4256, 2302, 676, 1482, 7617, 20398, 20398, 7617, 1482, 3249, 21707, 98575, 150862, 98575, 21707, 3249, 6840, 62070, 397340, 1155953, 1155953, 397340, 62070, 6840, 14400, 160219, 1623115
Offset: 1

Views

Author

R. H. Hardin, Jan 10 2014

Keywords

Comments

Table starts
....16.....44......121........286...........676............1482
....44....172......704.......2302..........7617...........21707
...121....704.....4256......20398.........98575..........397340
...286...2302....20398.....150862.......1155953.........7379380
...676...7617....98575....1155953......13930916.......145005714
..1482..21707...397340....7379380.....145005714......2573684600
..3249..62070..1623115...48788187....1561049902.....48150637857
..6840.160219..5744912..273307984...14369333157....775525688659
.14400.413728.20612708.1578043496..137304769214..13190905086499
.29640.994013.65877470.7881635316.1126706100728.190687328015653

Examples

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

Links

Crossrefs

Column 1 is A204032

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
k=2: [order 31]
k=3: [order 73]

A238255 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with 2X2 subblock sums lexicographically nondecreasing columnwise and rowwise.

Original entry on oeis.org

16, 44, 44, 121, 180, 121, 286, 804, 804, 286, 676, 2818, 6828, 2818, 676, 1482, 9991, 43456, 43456, 9991, 1482, 3249, 29995, 284992, 523578, 284992, 29995, 3249, 6840, 90225, 1473792, 6683137, 6683137, 1473792, 90225, 6840, 14400, 241945, 7616082
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2014

Keywords

Comments

Table starts
....16......44.......121..........286.............676.............1482
....44.....180.......804.........2818............9991............29995
...121.....804......6828........43456..........284992..........1473792
...286....2818.....43456.......523578.........6683137.........65450601
...676....9991....284992......6683137.......171041320.......3320993180
..1482...29995...1473792.....65450601......3320993180.....128727296869
..3249...90225...7616082....640472606.....64353451945....5017308028639
..6840..241945..32986844...5080416791....992794904591..154350327958339
.14400..649320.142361644..40066932588..15160526139045.4704917436206270
.29640.1605951.537301496.267891545518.192941078342371

Examples

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

Links

Crossrefs

Column 1 is A204032

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) -18*a(n-3) +17*a(n-4) +22*a(n-5) -36*a(n-6) +20*a(n-8) -8*a(n-9)
k=2: [order 33]
k=3: [order 81]
Showing 1-3 of 3 results.

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