A241370 -id:A241370 - cp's OEIS frontend

A241364 Number of n X 2 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

1, 7, 47, 326, 2284, 16026, 112458, 789166, 5537942, 38862302, 272714782, 1913766030, 13429783278, 94243014094, 661346912462, 4640977825550, 32567892540814, 228543997497870, 1603799162836494, 11254602102332686

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

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

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

Column 2 of A241370.

Empirical: a(n) = 7*a(n-1) + 2*a(n-3) - 8*a(n-4) for n>5.

Empirical g.f.: x*(1 + x)*(1 - x - x^2 - 4*x^3) / ((1 - x)*(1 - 6*x - 6*x^2 - 8*x^3)). - Colin Barker, Oct 30 2018

A241365 Number of nX3 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

2, 28, 460, 7376, 118488, 1904096, 30598800, 491723328, 7902006144, 126985443680, 2040659387360, 32793449527584, 526991588462752, 8468768559462432, 136093331438385952, 2187023382674637856, 35145522751283965984

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 3 of A241370

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

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

Empirical: a(n) = 15*a(n-1) +18*a(n-2) -8*a(n-3) -68*a(n-4) -164*a(n-5) -256*a(n-6) -176*a(n-7) +64*a(n-8)

A241366 Number of nX4 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

4, 121, 4617, 169982, 6280325, 232173463, 8582759752, 317280724429, 11729003927933, 433589294151366, 16028613931818561, 592534154813233243, 21904372151717063740, 809744915865384534529, 29934061758919096085329

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 4 of A241370

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

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

Empirical: a(n) = 39*a(n-1) -89*a(n-2) +700*a(n-3) -7268*a(n-4) +12612*a(n-5) -23904*a(n-6) +125306*a(n-7) -773407*a(n-8) +79505*a(n-9) +3859531*a(n-10) -3389476*a(n-11) -9274781*a(n-12) +92305*a(n-13) +19760919*a(n-14) +25560786*a(n-15) -3646222*a(n-16) -31076228*a(n-17) -38721450*a(n-18) -14157300*a(n-19) +16466073*a(n-20) +30488603*a(n-21) +16120777*a(n-22) +778176*a(n-23) -4523626*a(n-24) -3303044*a(n-25) -267592*a(n-26) -1363088*a(n-27) -220864*a(n-28) +213504*a(n-29) -47104*a(n-30) +98304*a(n-31)

A241367 Number of nX5 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

8, 523, 46245, 3910194, 332185927, 28238828935, 2400505507498, 204061855414167, 17346886991310331, 1474623966935696590, 125354818374255514287, 10656161088317132650049, 905858830474955211374142

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 5 of A241370

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 94

Empirical recurrence of order 94 (see link above)

A241368 Number of nX6 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

16, 2261, 463567, 90008909, 17583615124, 3437694358689, 672068364873884, 131390467341043995, 25687100469219790719, 5021879971708227297466, 981787679524970561772746, 191941475758292573127986823

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 6 of A241370

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

R. H. Hardin, Table of n, a(n) for n = 1..185

A241369 Number of nX7 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

32, 9775, 4646421, 2071815945, 930716218752, 418470887683606, 188148208461270141, 84594118185093500244, 38034801930029063688859, 17101026608230289359891342, 7688882351945169694778666410

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Column 7 of A241370

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

R. H. Hardin, Table of n, a(n) for n = 1..43

A241371 Number of 2 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

2, 7, 28, 121, 523, 2261, 9775, 42261, 182711, 789933, 3415199, 14765285, 63836295, 275990109, 1193216815, 5158758677, 22303399319, 96426611981, 416891226559, 1802389311557, 7792457656743, 33689944754365, 145655251212111

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

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

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

Row 2 of A241370.

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 4*a(n-3) for n>5.

Empirical g.f.: x*(1 - x - x^2)*(2 - x - 2*x^2) / (1 - 5*x + 2*x^2 + 4*x^3). - Colin Barker, Oct 30 2018

A241372 Number of 3 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

5, 47, 460, 4617, 46245, 463567, 4646421, 46573979, 466838093, 4679401043, 46904463629, 470151838595, 4712616517773, 47237408834627, 473489150832621, 4746068456910627, 47572717892835405, 476850156780960707

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

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

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

Row 3 of A241370.

Empirical: a(n) = 9*a(n-1) + 16*a(n-2) - 50*a(n-3) - 72*a(n-4) - 32*a(n-5) - 32*a(n-6) for n>8.

Empirical g.f.: x*(5 + 2*x - 43*x^2 - 25*x^3 + 42*x^4 + 34*x^5 + 32*x^6 + 16*x^7) / (1 - 9*x - 16*x^2 + 50*x^3 + 72*x^4 + 32*x^5 + 32*x^6). - Colin Barker, Oct 30 2018

A241373 Number of 4Xn 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

14, 326, 7376, 169982, 3910194, 90008909, 2071815945, 47690157718, 1097756412666, 25268747760871, 581649645222695, 13388725521741539, 308188912773527912, 7094058807175007496, 163294876256510271215

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 4 of A241370

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

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

Empirical: a(n) = 32*a(n-1) -214*a(n-2) +26*a(n-3) +3879*a(n-4) -15470*a(n-5) +19107*a(n-6) +72463*a(n-7) -211026*a(n-8) +106996*a(n-9) +193844*a(n-10) -2000756*a(n-11) +412552*a(n-12) +8652096*a(n-13) -3035456*a(n-14) -10691648*a(n-15) +6530688*a(n-16) +2014720*a(n-17) -6114304*a(n-18) +2244608*a(n-19) +1933312*a(n-20) -720896*a(n-21) for n>23

A241374 Number of 5Xn 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Original entry on oeis.org

41, 2284, 118488, 6280325, 332185927, 17583615124, 930716218752, 49265035135614, 2607715881819884, 138032784674740932, 7306413606898346790, 386746399853598819698, 20471436010315498503254, 1083603347076782168624072

Offset: 1

R. H. Hardin, Apr 20 2014

nonn

Row 5 of A241370

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 65

Empirical recurrence of order 65 (see link above)

cp's OEIS Frontend

A241364 Number of n X 2 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241365 Number of nX3 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241366 Number of nX4 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241367 Number of nX5 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241368 Number of nX6 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

A241369 Number of nX7 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

A241371 Number of 2 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241372 Number of 3 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241373 Number of 4Xn 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241374 Number of 5Xn 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.

Views

Author

Keywords

Comments

Examples

Links

Formula