A208872 -id:A208872 - cp's OEIS frontend

A208866 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

2, 12, 143, 1979, 28246, 405481, 5826959, 83752328, 1203835147, 17303737555, 248721498050, 3575088704597, 51387836750983, 738641752044964, 10617135747615911, 152609260439813291, 2193584684852893774

Offset: 1

R. H. Hardin, Mar 02 2012

nonn

Column 2 of A208872.

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

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

Cf. A208872.

Empirical: a(n) = 18*a(n-1) - 55*a(n-2) + 42*a(n-3) - 9*a(n-4) for n>5.

Empirical g.f.: x*(2 - 24*x + 37*x^2 - 19*x^3 + 3*x^4) / ((1 - 3*x + x^2)*(1 - 15*x + 9*x^2)). - Colin Barker, Jul 07 2018

A208867 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

5, 136, 6520, 324682, 16205218, 808928836, 40380275500, 2015711853262, 100620769519078, 5022810805035976, 250729829501722000, 12515989521112631602, 624776054783641480618, 31187715359825604175756

Offset: 1

R. H. Hardin, Mar 02 2012

nonn

Column 3 of A208872.

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

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

Cf. A208872.

Empirical: a(n) = 55*a(n-1) -261*a(n-2) +369*a(n-3) -162*a(n-4) for n>5.

Empirical g.f.: x*(5 - 139*x + 345*x^2 - 267*x^3 + 54*x^4) / ((1 - x)*(1 - 3*x)*(1 - 51*x + 54*x^2)). - Colin Barker, Jul 07 2018

A208868 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

15, 1798, 307165, 52947540, 9130195864, 1574432811027, 271499374919883, 46818078167209471, 8073434644321782464, 1392204668383719239473, 240075497495975972163390, 41399261047580372916745574

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 4 of A208872

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

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

Empirical: a(n) = 198*a(n-1) -4637*a(n-2) +40574*a(n-3) -164314*a(n-4) +321776*a(n-5) -281785*a(n-6) +85300*a(n-7) -8100*a(n-8) for n>9

A208869 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

51, 24472, 14493405, 8624977114, 5134914951163, 3057224057476808, 1820216057105650386, 1083724145919960847502, 645230025599333921071976, 384158448692090971917060268, 228721088397696942173901117684

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 5 of A208872

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

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

Empirical: a(n) = 698*a(n-1) -64930*a(n-2) +2349972*a(n-3) -40985428*a(n-4) +382137700*a(n-5) -2071312484*a(n-6) +7427716824*a(n-7) -22247002672*a(n-8) +65755191408*a(n-9) -163887803568*a(n-10) +277785052512*a(n-11) -285817496832*a(n-12) +164238606720*a(n-13) -46819296000*a(n-14) +4897760256*a(n-15) for n>16

A208870 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

187, 334618, 683903931, 1404920207834, 2887736845657700, 5935974611645510227, 12201956787655438957014, 25082292111547260024518313, 51559059416667161930347967813, 105984596999356698511898369562313

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 6 of A208872

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

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

A208871 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

715, 4578580, 32271626438, 228847686794351, 1624001903270517563, 11525604443642285224422, 81798476241280856702695038, 580533377647449287012352167379, 4120113916814898485216382089787455

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Column 7 of A208872

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

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

A208873 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

2, 12, 136, 1798, 24472, 334618, 4578580, 62655190, 857412640, 11733394642, 160567489036, 2197311225838, 30069453572632, 411490201499818, 5631102858140740, 77059719245016070, 1054535937228511120

Offset: 1

R. H. Hardin, Mar 02 2012

nonn

Row 2 of A208872.

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

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

Cf. A208872.

Empirical: a(n) = 18*a(n-1) - 65*a(n-2) + 84*a(n-3) - 36*a(n-4) for n>5.

Empirical g.f.: 2*x*(1 - 12*x + 25*x^2 - 19*x^3 + 6*x^4) / ((1 - x)*(1 - 2*x)*(1 - 15*x + 18*x^2)). - Colin Barker, Jul 07 2018

A208874 Number of 3Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

5, 143, 6520, 307165, 14493405, 683903931, 32271626438, 1522813452263, 71857577327143, 3390770839381669, 160001593732718856, 7550056082308516761, 356267369073405009281, 16811323900505484274607, 793282337427660173475274

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Row 3 of A208872

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

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

Empirical: a(n) = 61*a(n-1) -722*a(n-2) +3476*a(n-3) -7851*a(n-4) +8583*a(n-5) -4266*a(n-6) +720*a(n-7) for n>8

A208875 Number of 4Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

15, 1979, 324682, 52947540, 8624977114, 1404920207834, 228847686794351, 37277070892199501, 6072074518379364073, 989082262060956074133, 161111942886719306980432, 26243578660069203997974518

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Row 4 of A208872

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

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

Empirical: a(n) = 222*a(n-1) -10949*a(n-2) +228692*a(n-3) -2273610*a(n-4) +10170544*a(n-5) -13839646*a(n-6) -45418980*a(n-7) +225253855*a(n-8) -439046430*a(n-9) +509809347*a(n-10) -407061936*a(n-11) +239595084*a(n-12) -96068592*a(n-13) +18662400*a(n-14) for n>16

A208876 Number of 5Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Original entry on oeis.org

51, 28246, 16205218, 9130195864, 5134914951163, 2887736845657700, 1624001903270517563, 913306247364608338853, 513625349165806029159816, 288852734835443348518960257, 162445063843968446617446229944

Offset: 1

R. H. Hardin Mar 02 2012

nonn

Row 5 of A208872

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

R. H. Hardin, Table of n, a(n) for n = 1..202

Empirical: a(n) = 835*a(n-1) -183323*a(n-2) +18547299*a(n-3) -987322450*a(n-4) +26936215656*a(n-5) -259592930108*a(n-6) -3698904511972*a(n-7) +105056981064194*a(n-8) -468082290224790*a(n-9) -8220453963894770*a(n-10) +93015305289328522*a(n-11) -3009215708038944*a(n-12) -4338208630525451740*a(n-13) +17757865170412343388*a(n-14) +59736218122280906604*a(n-15) -622267506833186033977*a(n-16) +938869955167775461259*a(n-17) +8000262558220637738773*a(n-18) -56634053288703764393173*a(n-19) +209139140116278936305898*a(n-20) -546065890364575413337540*a(n-21) +1008121942435233118210008*a(n-22) -1160912061971582376908448*a(n-23) +524709510887340807606720*a(n-24) +511243927003064543493888*a(n-25) -896720906468773868608512*a(n-26) +430645964613584885342208*a(n-27) +74415201590159365275648*a(n-28) -159217853403663932719104*a(n-29) +60721875388690274451456*a(n-30) -7836898836947747733504*a(n-31) for n>34

cp's OEIS Frontend

A208866 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208867 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208868 Number of nX4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208869 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208870 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

A208871 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

A208873 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 one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A208874 Number of 3Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208875 Number of 4Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples

Links

Formula

A208876 Number of 5Xn 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

Views

Author

Keywords

Comments

Examples