A208408 -id:A208408 - cp's OEIS frontend

A208401 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

1, 15, 10682, 163422914, 39216100214432, 146298576850884166522, 8484183047877022205116428184, 7648479804732030712438650610523878146, 107185313935414834818609318544471943157967376388

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Diagonal of A208408.

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

R. H. Hardin, Table of n, a(n) for n = 1..13

Cf. A208408.

A208402 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

2, 15, 187, 2795, 43947, 700075, 11188907, 178973355, 2863377067, 45813246635, 733008800427, 11728128223915, 187650001250987, 3002399818689195, 48038396293720747, 768614337478306475, 12297829386768001707

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Column 2 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3).
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: x*(2 - 27*x + 40*x^2) / ((1 - x)*(1 - 4*x)*(1 - 16*x)).
a(n) = (8 + 3*2^(1+2*n) + 16^n) / 24.
(End)

A208403 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

5, 182, 10682, 667478, 42012698, 2646531062, 166729574522, 10503950018198, 661748758909658, 41690171165650742, 2626480778916392762, 165468289040095516118, 10424502209304556920218, 656743639184636861807222

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Column 3 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 70*a(n-1) - 441*a(n-2) for n>3.
Conjectures from Colin Barker, Jul 02 2018: (Start)
G.f.: x*(5 - 168*x + 147*x^2) / ((1 - 7*x)*(1 - 63*x)).
a(n) = (2/27)*7^(-1+n) * (27+4*9^n) for n>1.
(End)

A208404 Number of n X 4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

15, 2698, 658450, 163422914, 40595679634, 10084768380770, 2505261257850802, 622357842865595522, 154606345205565641170, 38407360426219085921186, 9541169432411414821885426, 2370220528768971149166621890

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Column 4 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 262*a(n-1) - 3385*a(n-2) + 2868*a(n-3) - 576*a(n-4) for n>5.

Empirical g.f.: x*(15 - 1232*x + 2349*x^2 - 1276*x^3 + 192*x^4) / ((1 - 13*x + 4*x^2)*(1 - 249*x + 144*x^2)). - Colin Barker, Jul 02 2018

A208405 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

51, 41914, 40883360, 40039156736, 39216100214432, 38410047476679936, 37620564383817645696, 36847308431734650845696, 36089946042522268966513152, 35348150537672718536490582016, 34621601954234065647421901637632

Offset: 1

R. H. Hardin Feb 26 2012

nonn

Column 5 of A208408

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

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

Empirical: a(n) = 1008*a(n-1) -28108*a(n-2) +138160*a(n-3) -223680*a(n-4) +168192*a(n-5) -55296*a(n-6) for n>7

A208406 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

187, 658450, 2540446156, 9810325806914, 37884515848419250, 146298576850884166522, 564960990903273888822194, 2181708996196484728947116626, 8425102300382037852914721068050

Offset: 1

R. H. Hardin Feb 26 2012

nonn

Column 6 of A208408

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

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

Empirical: a(n) = 3934*a(n-1) -280797*a(n-2) +6155504*a(n-3) -54994340*a(n-4) +272040900*a(n-5) -839264272*a(n-6) +1746698176*a(n-7) -2573895744*a(n-8) +2742227712*a(n-9) -2077701120*a(n-10) +970113024*a(n-11) -191102976*a(n-12) for n>13

A208407 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

715, 10370330, 157873031498, 2403711876698218, 36598079445605633928, 557229580446475130201608, 8484183047877022205116428184, 129177209027669581083328287797640, 1966807085374417176424317546443585928

Offset: 1

R. H. Hardin Feb 26 2012

nonn

Column 7 of A208408

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

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

A208409 Number of 2 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

2, 15, 182, 2698, 41914, 658450, 10370330, 163422914, 2575668586, 40595679634, 639841707002, 10084768380770, 158949607034890, 2505261257850802, 39486313909133978, 622357842865595522, 9809203406810575786

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Row 2 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 18*a(n-1) - 31*a(n-2) - 66*a(n-3) - 24*a(n-4) for n>6.

Empirical g.f.: x*(1 + x)*(2 - 23*x - 3*x^2 + 22*x^3 + 8*x^4) / ((1 - 3*x - 2*x^2)*(1 - 15*x - 12*x^2)). - Colin Barker, Jul 02 2018

A208410 Number of 3 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

5, 187, 10682, 658450, 40883360, 2540446156, 157873031498, 9810914663050, 609693293454056, 37889020302613060, 2354590230800815490, 146324584692741696562, 9093252748398554214416, 565094688091663621180732

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Row 3 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 62*a(n-1) + 39*a(n-2) - 1790*a(n-3) - 4703*a(n-4) - 1254*a(n-5) + 3249*a(n-6) + 918*a(n-7) - 648*a(n-8) for n>10.

Empirical g.f.: x*(1 + x)*(2 - 23*x - 3*x^2 + 22*x^3 + 8*x^4) / ((1 - 3*x - 2*x^2)*(1 - 15*x - 12*x^2)). - Colin Barker, Jul 02 2018

A208411 Number of 4 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

15, 2795, 667478, 163422914, 40039156736, 9810325806914, 2403711876698218, 588954110860577394, 144304709913279198696, 35357337571782719886214, 8663205247528271356492160, 2122646395773319892200238358

Offset: 1

R. H. Hardin, Feb 26 2012

nonn

Row 4 of A208408.

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

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

Cf. A208408.

Empirical: a(n) = 226*a(n-1) +4747*a(n-2) -18294*a(n-3) -739509*a(n-4) -1661510*a(n-5) +17227605*a(n-6) +10151090*a(n-7) -98711047*a(n-8) -11588022*a(n-9) +195980121*a(n-10) -44074854*a(n-11) -121060656*a(n-12) +71173728*a(n-13) -10077696*a(n-14) for n>16.

cp's OEIS Frontend

A208401 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A208402 Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208403 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208404 Number of n X 4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208405 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208406 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208407 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

A208409 Number of 2 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208410 Number of 3 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208411 Number of 4 X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author