A209744 -id:A209744 - cp's OEIS frontend

A209738 Number of n X 2 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

2, 6, 57, 700, 10594, 183240, 3412100, 65953664, 1298076552, 25767620512, 513555943312, 10254450363264, 204934235829536, 4097247120151424, 81931587030997056, 1638507658307430400, 32769000295781617792

Offset: 1

R. H. Hardin, Mar 12 2012

nonn

Column 2 of A209744.

			Some solutions for n=5:
..0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..1....0..1....0..0
..1..2....1..2....1..2....0..2....1..2....1..2....1..2....2..0....1..2....1..2
..0..0....0..0....2..0....0..3....1..0....0..0....2..0....0..3....0..0....1..3
..1..2....3..1....3..0....0..1....0..2....2..3....2..1....2..2....1..2....2..1
..1..3....4..1....0..4....0..2....0..1....2..4....2..0....0..1....1..0....3..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A209744.

Empirical: a(n) = 32*a(n-1) - 258*a(n-2) + 296*a(n-3) + 1256*a(n-4) + 480*a(n-5) for n>6.

Empirical g.f.: x*(2 - 58*x + 381*x^2 - 168*x^3 - 1388*x^4 - 536*x^5) / ((1 - 20*x)*(1 - 4*x - 2*x^2)*(1 - 8*x - 12*x^2)). - Colin Barker, Jul 12 2018

A209739 Number of n X 3 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

5, 57, 2025, 103373, 6262064, 404495219, 26715084257, 1777603386801, 118573281463225, 7915782848604211, 528589085007311295, 35300530985616790273, 2357529150039721810029, 157447991892723989479547

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Column 3 of A209744.

			Some solutions for n=5
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..1..2..1....1..2..3....1..2..1....1..2..1....1..2..1....1..2..1....1..2..1
..0..0..0....3..1..1....1..0..0....0..0..1....3..3..1....2..0..0....3..3..2
..1..3..4....4..3..0....1..2..3....1..2..1....0..1..2....0..3..4....2..4..2
..1..5..3....5..3..1....0..0..3....0..0..0....0..3..1....0..5..4....0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A209744.

Empirical: a(n) = 100*a(n-1) -2365*a(n-2) +6020*a(n-3) +291532*a(n-4) -2681320*a(n-5) +4701820*a(n-6) +23602304*a(n-7) -82586672*a(n-8) +27026368*a(n-9) +113762816*a(n-10) -78159872*a(n-11) +7864320*a(n-12) for n>13.

A209740 Number of nX4 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

15, 700, 103373, 20611956, 4474325828, 991613495404, 220845828478730, 49242046909442868, 10982471712866182098, 2449579228342732267816, 546373088082223670747386, 121867698385924682716244064

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Column 4 of A209744

			Some solutions for n=5
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..0....0..0..0..0
..1..2..3..2....1..2..1..2....1..2..1..2....1..2..0..2....1..2..1..2
..4..1..1..1....0..0..2..3....0..1..3..3....0..1..2..3....0..0..0..2
..4..3..4..0....1..2..1..1....3..0..0..1....4..4..1..1....3..1..2..4
..5..4..5..0....4..4..4..2....0..4..1..4....5..3..3..2....5..3..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 244*a(n-1) +137*a(n-2) -1195614*a(n-3) +21837944*a(n-4) +1404675270*a(n-5) -36835307408*a(n-6) -326873376252*a(n-7) +14507648154376*a(n-8) -8311682181464*a(n-9) -2334523810998832*a(n-10) +8762975100490480*a(n-11) +185277092995650336*a(n-12) -908553103605691712*a(n-13) -8222060623354335360*a(n-14) +40603092591766507264*a(n-15) +222543140644632005632*a(n-16) -906919532901077344256*a(n-17) -3774725396673218404352*a(n-18) +10011737555551519784960*a(n-19) +37478635910651820179456*a(n-20) -48928099712667888910336*a(n-21) -182050232765906369380352*a(n-22) +115193182556326721486848*a(n-23) +411251029796589926350848*a(n-24) -170990851031162490454016*a(n-25) -418387866292483163947008*a(n-26) +167007575033595637530624*a(n-27) +154943201526404521918464*a(n-28) -70873530141897822044160*a(n-29) for n>30

A209741 Number of nX5 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

52, 10594, 6262064, 4474325828, 3309942226828, 2462887498725440, 1834383283218723590, 1366486932112899379170, 1017964144833296194871291, 758335528163948847329102970, 564924804927465477617885477572

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Column 5 of A209744

			Some solutions for n=5
..0..0..0..0..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..2..3..1..2....1..2..1..2..1....1..2..1..2..1....1..2..1..2..3
..0..0..3..0..0....0..0..0..0..0....1..3..3..1..3....4..1..3..1..1
..1..2..0..4..1....1..2..1..2..1....3..0..1..4..1....3..1..0..0..2
..4..2..5..4..5....0..0..1..0..0....4..0..2..4..5....5..5..5..4..0

R. H. Hardin, Table of n, a(n) for n = 1..210

A209742 Number of nX6 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

203, 183240, 404495219, 991613495404, 2462887498725440, 6126537051572916244, 15242797658314710633378, 37924827001459049241306782, 94359067187520965488130465180, 234770648430435211602772504683016

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Column 6 of A209744

			Some solutions for n=5
..0..0..0..0..0..0....0..0..0..0..0..0....0..1..0..0..1..0....0..0..1..2..1..0
..1..2..1..3..2..1....1..2..1..2..1..3....2..0..2..1..2..0....1..3..0..0..0..2
..3..1..0..0..0..1....3..1..3..3..1..0....2..1..0..0..2..1....0..0..4..1..4..2
..2..3..1..2..3..0....3..0..0..1..0..4....0..1..2..3..0..0....5..2..4..2..1..2
..0..2..2..0..2..2....5..5..3..3..0..1....2..1..0..0..1..2....1..5..4..5..1..5

R. H. Hardin, Table of n, a(n) for n = 1..210

A209743 Number of nX7 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

876, 3412100, 26715084257, 220845828478730, 1834383283218723590, 15242797658314710633378, 126664397726626418134051983, 1052557322792113887592378377140, 8746556030412972768884396379035027

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Column 7 of A209744

			Some solutions for n=5
..0..0..0..1..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..1..2..3..3..3..4..5....1..2..3..2..1..2..1....1..2..3..1..2..3..4
..1..0..0..2..0..3..3....3..1..1..1..3..1..3....5..5..2..2..4..2..4
..4..1..2..4..2..0..1....2..2..0..2..1..2..3....0..4..4..5..5..2..3
..1..5..2..1..1..0..4....0..1..0..3..2..4..4....0..5..0..0..1..5..3

R. H. Hardin, Table of n, a(n) for n = 1..14

A209737 Number of n X n 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

Original entry on oeis.org

1, 6, 2025, 20611956, 3309942226828, 6126537051572916244, 126664397726626418134051983

Offset: 1

R. H. Hardin Mar 12 2012

nonn

Diagonal of A209744

			Some solutions for n=5
..0..0..0..0..1....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
..1..2..1..2..0....1..2..1..2..0....1..2..1..2..1....1..2..1..2..1
..0..1..0..0..3....1..0..0..0..3....0..0..0..0..0....0..1..0..2..3
..1..2..1..2..2....3..3..4..1..0....1..2..1..2..1....1..4..4..0..2
..0..2..3..1..0....1..4..5..4..0....0..0..1..0..0....5..5..2..0..1

cp's OEIS Frontend

A209738 Number of n X 2 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209739 Number of n X 3 0..5 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209740 Number of nX4 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209741 Number of nX5 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209742 Number of nX6 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209743 Number of nX7 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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A209737 Number of n X n 0..5 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..5 introduced in row major order.

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