A222555 -id:A222555 - cp's OEIS frontend

A222549 Number of (n+2) X 1 arrays of occupancy after each element moves up to +-2 places but not 0.

7, 20, 64, 208, 651, 2056, 6496, 20483, 64627, 203905, 643272, 2029453, 6402679, 20199560, 63726952, 201050056, 634285971, 2001087460, 6313163200, 19917184799, 62836052203, 198239333473, 625418559696, 1973111833705, 6224903700199

Offset: 1

R. H. Hardin, Feb 24 2013

nonn

Column 2 of A222555.

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

R. H. Hardin, Table of n, a(n) for n = 1..147

Cf. A222555.

Empirical: a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) - 8*a(n-4) + 12*a(n-5) - 3*a(n-6) - a(n-7).

Empirical g.f.: x*(7 - 15*x + 6*x^2 - 6*x^3 + 11*x^4 - 3*x^5 - x^6) / ((1 - x)*(1 - 4*x + 2*x^2 + 8*x^4 - 4*x^5 - x^6)). - Colin Barker, Aug 16 2018

A222550 Number of (n+3) X 1 arrays of occupancy after each element moves up to +-3 places but not 0.

Original entry on oeis.org

31, 102, 359, 1279, 4537, 15929, 56041, 197313, 694561, 2443809, 8598567, 30254246, 106446779, 374510087, 1317616614, 4635657529, 16309130459, 57378359687, 201866467555, 710197956209, 2498584711494, 8790394014302, 30925899907467

Offset: 1

R. H. Hardin, Feb 24 2013

nonn

Column 3 of A222555.

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

R. H. Hardin, Table of n, a(n) for n = 1..131

Cf. A222555.

Empirical: a(n) = 7*a(n-1) -15*a(n-2) +10*a(n-3) +4*a(n-4) -36*a(n-5) +73*a(n-6) -29*a(n-7) -21*a(n-8) -a(n-9).

Empirical g.f.: x*(31 - 115*x + 110*x^2 - 14*x^3 - 175*x^4 + 473*x^5 - 224*x^6 - 148*x^7 - 7*x^8) / (1 - 7*x + 15*x^2 - 10*x^3 - 4*x^4 + 36*x^5 - 73*x^6 + 29*x^7 + 21*x^8 + x^9). - Colin Barker, Aug 16 2018

A222551 Number of (n+4)X1 arrays of occupancy after each element moves up to +-4 places but not 0.

Original entry on oeis.org

121, 427, 1562, 5761, 21239, 78245, 287858, 1059674, 3901868, 14366833, 52894813, 194725954, 716822517, 2638639647, 9712504051, 35749337667, 131581046318, 484294944395, 1782459967105, 6560310404375, 24144873322163, 88863279809958

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Column 4 of A222555

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

R. H. Hardin, Table of n, a(n) for n = 1..117

Empirical: a(n) = 9*a(n-1) -28*a(n-2) +35*a(n-3) -15*a(n-4) +12*a(n-5) -96*a(n-6) +274*a(n-7) -265*a(n-8) +24*a(n-9) -7*a(n-10) +29*a(n-11) +3*a(n-12) -a(n-13)

A222552 Number of (n+5)X1 arrays of occupancy after each element moves up to +-5 places but not 0.

Original entry on oeis.org

456, 1668, 6220, 23341, 87752, 330274, 1244135, 4688684, 17678240, 66670133, 251457191, 948433758, 3577222198, 13491914845, 50884787739, 191905944304, 723728206116, 2729294349873, 10292348908806, 38812294765020

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Column 5 of A222555

			Some solutions for n=3
..0....2....1....0....0....1....1....0....0....3....0....0....1....1....0....0
..0....0....2....1....2....0....6....0....0....0....3....0....0....0....0....4
..3....0....1....1....2....0....0....0....1....1....0....4....2....2....0....0
..3....2....1....0....0....4....0....0....0....1....0....0....0....0....2....1
..0....2....0....5....1....1....0....4....0....0....0....0....0....0....1....3
..1....0....0....0....1....0....0....0....1....1....2....4....1....3....0....0
..0....0....3....1....0....1....1....2....3....2....0....0....2....2....2....0
..1....2....0....0....2....1....0....2....3....0....3....0....2....0....3....0

R. H. Hardin, Table of n, a(n) for n = 1..71

Empirical: a(n) = 11*a(n-1) -45*a(n-2) +84*a(n-3) -70*a(n-4) +21*a(n-5) +18*a(n-6) -200*a(n-7) +753*a(n-8) -1183*a(n-9) +631*a(n-10) +8*a(n-11) -2*a(n-12) +58*a(n-13) -32*a(n-14) -6*a(n-15)

A222553 Number of (n+6)X1 arrays of occupancy after each element moves up to +-6 places but not 0.

Original entry on oeis.org

1709, 6372, 24024, 91052, 346091, 1318249, 5029086, 19207812, 73418105, 280780468, 1074200514, 4110562320, 15731749698, 60212701130, 230472089415

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Column 6 of A222555

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

A222554 Number of (n+7)X1 arrays of occupancy after each element moves up to +-7 places but not 0.

Original entry on oeis.org

6427, 24230, 92011, 350967, 1342944, 5151294, 19797737, 76201719, 293634727, 1132449121, 4370239031, 16873077353

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Column 7 of A222555

			Some solutions for n=2
..1....1....0....2....0....2....2....0....1....2....0....3....1....1....0....0
..0....0....1....4....2....1....4....2....1....0....0....0....1....1....0....1
..2....5....0....0....0....1....2....1....4....3....1....1....0....0....0....0
..0....0....3....3....0....1....0....1....0....0....0....0....0....2....2....4
..1....0....1....0....0....1....1....1....0....0....0....3....2....1....1....0
..0....1....1....0....1....1....0....0....1....0....0....1....1....0....2....0
..1....2....0....0....4....0....0....1....1....4....6....0....0....3....0....2
..3....0....0....0....0....0....0....0....0....0....2....1....2....1....4....1
..1....0....3....0....2....2....0....3....1....0....0....0....2....0....0....1

A222556 Number of (n+2)X1 arrays of occupancy after each element moves up to +-n places but not 0.

Original entry on oeis.org

2, 20, 102, 427, 1668, 6372, 24230, 92279, 352596

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Row 2 of A222555

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

A222557 Number of (n+3)X1 arrays of occupancy after each element moves up to +-n places but not 0.

Original entry on oeis.org

4, 64, 359, 1562, 6220, 24024, 92011, 352258, 1351519

Offset: 1

R. H. Hardin Feb 24 2013

nonn

Row 3 of A222555

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

cp's OEIS Frontend

A222549 Number of (n+2) X 1 arrays of occupancy after each element moves up to +-2 places but not 0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A222550 Number of (n+3) X 1 arrays of occupancy after each element moves up to +-3 places but not 0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A222551 Number of (n+4)X1 arrays of occupancy after each element moves up to +-4 places but not 0.

Views

Author

Keywords

Comments

Examples

Links

Formula

A222552 Number of (n+5)X1 arrays of occupancy after each element moves up to +-5 places but not 0.

Views

Author

Keywords

Comments

Examples

Links

Formula

A222553 Number of (n+6)X1 arrays of occupancy after each element moves up to +-6 places but not 0.

Views

Author

Keywords

Comments

Examples

A222554 Number of (n+7)X1 arrays of occupancy after each element moves up to +-7 places but not 0.

Views

Author

Keywords

Comments

Examples

A222556 Number of (n+2)X1 arrays of occupancy after each element moves up to +-n places but not 0.

Views

Author

Keywords

Comments

Examples

A222557 Number of (n+3)X1 arrays of occupancy after each element moves up to +-n places but not 0.

Views

Author

Keywords

Comments

Examples