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.

A224173 T(n,k) = number of n X k 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

4, 16, 10, 50, 100, 20, 130, 684, 400, 35, 296, 3526, 4739, 1225, 56, 610, 14751, 38561, 22988, 3136, 84, 1163, 52591, 242114, 272130, 87878, 7056, 120, 2083, 165212, 1253770, 2335459, 1460836, 282372, 14400, 165, 3544, 468292, 5588411, 15925611
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2013

Keywords

Examples

			Table starts:
    4    16       50       130         296          610           1163
   10   100      684      3526       14751        52591         165212
   20   400     4739     38561      242114      1253770        5588411
   35  1225    22988    272130     2335459     15925611       91494280
   56  3136    87878   1460836    16625026    143558572     1012166273
   84  7056   282372   6425876    95808564   1038484760     8857798353
  120 14400   794220  24197608   468021427   6360047093    65713691148
  165 27225  2010035  80350989  1994287334  33901838632   426013124302
  220 48400  4668304 240416852  7568051210 160168789130  2451904991177
  286 81796 10095924 658890738 25994968917 680269560125 12667946702827
  ...
Some solutions for n=3 k=4
..0..0..1..0....0..0..1..2....0..0..3..0....0..2..0..0....0..3..3..1
..1..3..3..1....0..1..3..2....3..3..3..1....1..2..0..0....1..3..3..1
..1..3..3..3....0..3..3..2....3..3..3..2....2..2..1..0....1..3..3..3

Links

Crossrefs

Main diagonal is A224167.
Columns 1..7 are A000292(n+1), A001249, A224168, A224169, A224170, A224171, A224172.
Rows 1..7 are A223659, A223865, A224174, A224175, A224176, A224177, A224178.
Cf. A223838.

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,3,6,9,12.
Empirical: rows n=1..5 are polynomials of degree 6*n for k>0,0,0,2,6.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A223987 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

4, 16, 10, 50, 100, 20, 130, 684, 400, 35, 296, 3526, 5029, 1225, 56, 610, 14751, 44803, 25410, 3136, 84, 1163, 52591, 308470, 358118, 99634, 7056, 120, 2083, 165212, 1738756, 3770722, 2086196, 325120, 14400, 165, 3544, 468292, 8350154, 31585056
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Table starts
...4....16.......50........130.........296...........610...........1163
..10...100......684.......3526.......14751.........52591.........165212
..20...400.....5029......44803......308470.......1738756........8350154
..35..1225....25410.....358118.....3770722......31585056......219861244
..56..3136....99634....2086196....31831914.....378122264.....3661410444
..84..7056...325120....9647292...204647416....3322756326....43307637038
.120.14400...922768...37395816..1067023886...22985966340...392525216516
.165.27225..2346883..126087157..4710529013..131366850521..2873859236297
.220.48400..5462600..379654704.18159308422..642224541548.17659521902693
.286.81796.11818092.1040942916.62548820489.2756467192963.93729371629362

Examples

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

Links

Crossrefs

Column 1 is A000292(n+1)
Column 2 is A001249
Row 1 is A223659
Row 2 is A223865

Formula

Empirical: columns k=1..7 are polynomials of degree 3*k
Empirical: rows n=1..7 are polynomials of degree 6*n

A224190 T(n,k) = Number of n X k 0..2 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

3, 9, 6, 22, 36, 10, 46, 158, 100, 15, 86, 548, 684, 225, 21, 148, 1600, 3526, 2205, 441, 28, 239, 4102, 14751, 15779, 5852, 784, 36, 367, 9503, 52591, 89380, 55438, 13524, 1296, 45, 541, 20299, 165212, 422488, 408222, 163746, 28176, 2025, 55, 771, 40570
Offset: 1

Views

Author

R. H. Hardin Apr 01 2013

Keywords

Comments

Table starts
..3....9.....22......46.......86........148.........239..........367
..6...36....158.....548.....1600.......4102........9503........20299
.10..100....684....3526....14751......52591......165212.......468292
.15..225...2205...15779....89380.....422488.....1727738......6272940
.21..441...5852...55438...408222....2469182....12741432.....57644194
.28..784..13524..163746..1519738...11444292....72710554....400958714
.36.1296..28176..424326..4844576...44435746...340780382...2249643632
.45.2025..54153..992607.13669953..150015321..1366188661..10635858679
.55.3025..97570.2138488.34953776..452158538..4823267213..43724068755
.66.4356.166738.4305730.82399174.1240740774.15322738603.159999462711

Examples

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

Links

Crossrefs

Column 1 is A000217(n+1).
Column 2 is A000537(n+1).
Row 1 is A223718.
Row 2 is A223919.
Row 3 is A223865.

Formula

Empirical: columns k=1..7 are polynomials of degree 2*k.
Empirical: rows n=1..7 are polynomials of degree 4*n.
Showing 1-3 of 3 results.

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