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 1-8 of 8 results.

A205468 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

14, 48, 175, 677, 2709, 11143, 46709, 198483, 851317, 3674723, 15929949, 69254347, 301652741, 1315582371, 5742416845, 25079258843, 109571246421, 478835560339, 2092898539805, 9148671997707, 39994487184037, 174849254952131
Offset: 1

Views

Author

R. H. Hardin, Jan 27 2012

Keywords

Comments

Column 1 of A205475.

Examples

			Some solutions for n=4:
..0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..0
..0..1....0..1....0..1....1..1....1..0....0..0....1..2....1..2....0..2....1..2
..0..1....0..0....1..1....2..1....1..1....0..0....1..0....0..2....1..2....0..2
..1..1....1..0....0..0....1..1....2..2....0..0....2..2....0..1....0..0....0..1
..1..2....1..0....1..0....1..2....2..1....0..0....0..1....0..2....2..1....2..2
		

Crossrefs

Cf. A205475.

Formula

Empirical: a(n) = 9*a(n-1) - 21*a(n-2) - 11*a(n-3) + 66*a(n-4) - 6*a(n-5) - 36*a(n-6).
Empirical g.f.: x*(14 - 78*x + 37*x^2 + 264*x^3 - 105*x^4 - 180*x^5) / ((1 - x)*(1 - 3*x)*(1 - 2*x - 2*x^2)*(1 - 3*x - 6*x^2)). - Colin Barker, Mar 04 2018

A205469 Number of (n+1)X3 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

48, 263, 1548, 9654, 61978, 405702, 2686876, 17926060, 120146998, 807610262, 5438698312, 36669657896, 247432193154, 1670424338586, 11280890946852, 76200323465372, 514795456961870, 3478208969481038, 23502035785763264
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 2 of A205475

Examples

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

Formula

Empirical: a(n) = 16*a(n-1) -85*a(n-2) +142*a(n-3) +159*a(n-4) -676*a(n-5) +465*a(n-6) +298*a(n-7) -506*a(n-8) +220*a(n-9) -32*a(n-10)

A205470 Number of (n+1)X4 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

175, 1548, 14639, 147129, 1504556, 15614579, 162976758, 1709130780, 17963198743, 189127385194, 1993106187666, 21019022873891, 221754001074914, 2340228495931166, 24701472352877203, 260760556151955406
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 3 of A205475

Examples

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

Formula

Empirical: a(n) = 20*a(n-1) -75*a(n-2) -688*a(n-3) +5022*a(n-4) -496*a(n-5) -63723*a(n-6) +111258*a(n-7) +251463*a(n-8) -817674*a(n-9) -9180*a(n-10) +2101200*a(n-11) -1759426*a(n-12) -1578136*a(n-13) +2839836*a(n-14) -596208*a(n-15) -1049272*a(n-16) +620728*a(n-17) +18624*a(n-18) -96072*a(n-19) +24528*a(n-20) -1728*a(n-21)

A205471 Number of (n+1)X5 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

677, 9654, 147129, 2368164, 38649376, 637115198, 10546235416, 175062268404, 2910381717975, 48432892623689, 806480855084974, 13434383228654935, 223845611339717176, 3730339300748533737, 62171596821236304515
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 4 of A205475

Examples

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

Formula

Empirical: a(n) = 49*a(n-1) -861*a(n-2) +5021*a(n-3) +33602*a(n-4) -616384*a(n-5) +2159023*a(n-6) +13154843*a(n-7) -126262661*a(n-8) +166866281*a(n-9) +1911261129*a(n-10) -8190366005*a(n-11) -4199925495*a(n-12) +98595747627*a(n-13) -158149981614*a(n-14) -480297554430*a(n-15) +1810623448866*a(n-16) +73856868140*a(n-17) -8830642410840*a(n-18) +10313214783034*a(n-19) +20233405349590*a(n-20) -52335000413976*a(n-21) -5155452594933*a(n-22) +125085995184875*a(n-23) -89591754726765*a(n-24) -148493098940275*a(n-25) +234688188015153*a(n-26) +38812319081071*a(n-27) -279162204744067*a(n-28) +118502255969331*a(n-29) +160693504928624*a(n-30) -157107476872016*a(n-31) -21108318004391*a(n-32) +83650248017101*a(n-33) -23794461371173*a(n-34) -18974234968177*a(n-35) +12562468145490*a(n-36) +410664770730*a(n-37) -2327194771228*a(n-38) +521150033512*a(n-39) +137884941320*a(n-40) -72598222160*a(n-41) +5036772224*a(n-42) +2386207040*a(n-43) -520260992*a(n-44) +31264768*a(n-45)

A205472 Number of (n+1)X6 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

2709, 61978, 1504556, 38649376, 1002405121, 26272023365, 690109737187, 18179839278978, 479230888858502, 12644948875816236, 333720627683258097, 8810523515340428257, 232623501031146386321, 6142757563889683779852
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 5 of A205475

Examples

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

A205473 Number of (n+1)X7 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

11143, 405702, 15614579, 637115198, 26272023365, 1094476686239, 45724154665434, 1914758450334723, 80250258826348339, 3365536894872561413, 141181596884768969546, 5923561349136374628421, 248557182283520215199720
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 6 of A205475

Examples

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

A205474 Number of (n+1)X8 0..2 arrays with every 2X2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

46709, 2686876, 162976758, 10546235416, 690109737187, 45724154665434, 3037575583505983, 202436915929887731, 13498762783933351903, 900966011839550985373, 60138771941362142753965, 4015480503188389069062751
Offset: 1

Views

Author

R. H. Hardin Jan 27 2012

Keywords

Comments

Column 7 of A205475

Examples

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

A205467 Number of (n+1) X (n+1) 0..2 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..2 introduced in row major order.

Original entry on oeis.org

14, 263, 14639, 2368164, 1002405121, 1094476686239, 3037575583505983, 21477571401148556382, 385928233193168681488351
Offset: 1

Views

Author

R. H. Hardin, Jan 27 2012

Keywords

Comments

Diagonal of A205475.

Examples

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

Crossrefs

Cf. A205475.
Showing 1-8 of 8 results.