A295120 -id:A295120 - cp's OEIS frontend

A295115 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

3, 9, 26, 77, 226, 665, 1960, 5769, 16983, 49998, 147198, 433361, 1275825, 3756068, 11058011, 32555211, 95843749, 282167522, 830711657, 2445646047, 7200072866, 21197281911, 62405585330, 183724361820, 540891347189, 1592404221036

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

			Some solutions for n=7:
..0..1..1. .0..1..1. .0..0..0. .0..1..0. .0..0..0. .0..0..0. .0..1..1
..0..0..0. .0..0..0. .0..0..1. .1..1..1. .0..0..0. .0..0..1. .1..0..0
..0..0..0. .0..0..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1. .1..0..0
..0..1..1. .0..0..1. .0..0..0. .1..0..0. .1..0..0. .1..1..0. .0..1..1
..0..0..0. .1..0..1. .0..0..1. .1..0..0. .0..0..0. .0..0..0. .0..0..0
..0..1..1. .1..0..0. .0..0..1. .0..0..0. .0..0..0. .1..1..0. .1..0..0
..0..0..0. .0..1..1. .0..0..0. .0..1..1. .0..1..1. .0..0..0. .1..0..0

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

Column 3 of A295120.

Empirical: a(n) = a(n-1) + 3*a(n-2) + 5*a(n-3) + 7*a(n-4) + 7*a(n-5) - a(n-6) - 8*a(n-7) - 5*a(n-8) + a(n-10).

Empirical g.f.: x*(3 + 6*x + 8*x^2 + 9*x^3 + 5*x^4 - 6*x^5 - 10*x^6 - 4*x^7 + x^8 + x^9) / (1 - x - 3*x^2 - 5*x^3 - 7*x^4 - 7*x^5 + x^6 + 8*x^7 + 5*x^8 - x^10). - Colin Barker, Feb 22 2019

A295116 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Original entry on oeis.org

4, 20, 77, 326, 1373, 5793, 24347, 102398, 431050, 1813753, 7631302, 32111207, 135119039, 568549155, 2392325744, 10066404116, 42357266765, 178230161368, 749953993371, 3155644584471, 13278270334423, 55872091215736

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

Column 4 of A295120.

			Some solutions for n=7
..1..1..0..1. .0..0..0..0. .0..0..0..1. .0..1..1..0. .1..0..0..0
..0..0..0..1. .1..0..1..1. .0..0..0..1. .1..0..0..1. .1..0..0..1
..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..0..1. .0..0..0..1
..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..1..0..0
..0..1..1..0. .1..0..0..0. .0..0..1..0. .1..1..0..0. .0..0..0..0
..0..0..0..0. .1..0..0..1. .0..0..0..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..1

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

Cf. A295120.

Empirical: a(n) = a(n-1) +5*a(n-2) +22*a(n-3) +43*a(n-4) +52*a(n-5) +35*a(n-6) +35*a(n-7) +21*a(n-8) +14*a(n-9) +6*a(n-10) +9*a(n-11) -7*a(n-12) -a(n-14)

A295117 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Original entry on oeis.org

6, 41, 226, 1373, 8257, 49302, 295083, 1768323, 10586331, 63381624, 379549120, 2272625520, 13607838241, 81481468232, 487893203155, 2921396482557, 17492709806652, 104742608145023, 627176268025963, 3755397674479571

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

Column 5 of A295120.

			Some solutions for n=6
..1..0..0..1..1. .0..1..0..1..0. .0..1..1..0..1. .0..0..0..1..1
..1..0..1..0..0. .0..1..0..1..0. .1..0..0..0..1. .0..1..1..0..0
..0..1..1..1..0. .0..0..0..0..0. .1..0..0..0..0. .0..0..0..1..1
..0..0..1..0..0. .0..0..1..1..0. .0..0..0..1..0. .0..0..0..0..0
..0..0..0..0..0. .0..0..0..0..0. .1..1..0..1..0. .1..1..0..1..0
..1..1..0..1..1. .0..0..0..1..1. .0..0..0..0..0. .0..0..0..1..0

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

Cf. A295120.

Empirical: a(n) = 2*a(n-1) +11*a(n-2) +54*a(n-3) +109*a(n-4) +176*a(n-5) +169*a(n-6) -624*a(n-7) -2316*a(n-8) -805*a(n-9) +4070*a(n-10) +1147*a(n-11) -6289*a(n-12) -3027*a(n-13) +7703*a(n-14) +11476*a(n-15) -3556*a(n-16) -7917*a(n-17) +4301*a(n-18) +5017*a(n-19) +5146*a(n-20) -7555*a(n-21) -4779*a(n-22) -3722*a(n-23) -748*a(n-24) +3499*a(n-25) -6052*a(n-26) +3673*a(n-27) -3014*a(n-28) +3241*a(n-29) -1105*a(n-30) +156*a(n-31) -410*a(n-32) +136*a(n-33) -199*a(n-34) +138*a(n-35) -15*a(n-36) +51*a(n-37) -2*a(n-38) +2*a(n-39) -a(n-40)

A295118 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Original entry on oeis.org

9, 85, 665, 5793, 49302, 420519, 3590821, 30650456, 261518933, 2232138695, 19050970320, 162588578831, 1387635803762, 11842933188678, 101074697830670, 862633152321378, 7362232721371648, 62833751476788374, 536261351701937815

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

Column 6 of A295120.

			Some solutions for n=5
..0..0..1..1..0..0. .0..0..1..0..0..1. .1..0..0..1..1..0. .0..0..1..1..0..0
..1..0..0..0..0..1. .0..0..1..0..0..1. .1..0..0..0..0..1. .0..0..0..0..0..0
..1..0..1..1..0..1. .1..1..0..0..0..0. .0..1..1..0..0..1. .0..0..0..0..1..0
..0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..0..0..0. .0..0..0..1..1..1
..0..0..0..1..1..0. .0..0..0..0..0..0. .0..1..1..0..0..0. .0..0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 78

Cf. A295120.

Empirical recurrence of order 78 (see link above)

A295119 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Original entry on oeis.org

13, 178, 1960, 24347, 295083, 3590821, 43655680, 530696748, 6452840307, 78464174127, 953998068679, 11599362088138, 141035410432226, 1714816891986887, 20850061397844599, 253511401875888073

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

Column 7 of A295120.

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

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

Cf. A295120.

A295114 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1's.

Original entry on oeis.org

1, 5, 26, 326, 8257, 420519, 43655680, 9196006628, 3931962260999, 3413278465996124, 6014918791165296861, 21516997694119562490452, 156257115416099427263269042, 2303561969444050408142747347914

Offset: 1

R. H. Hardin, Nov 15 2017

nonn

Diagonal of A295120.

			Some solutions for n=5
..0..0..0..0..0. .1..0..0..1..1. .0..0..0..0..0. .0..0..0..0..1
..1..1..0..0..0. .1..0..1..0..0. .1..1..0..1..1. .0..0..0..0..1
..0..0..1..1..0. .0..1..1..1..0. .0..0..1..0..0. .0..0..0..0..0
..0..1..0..0..0. .0..0..1..0..1. .1..0..1..0..0. .0..0..0..0..1
..0..1..0..1..1. .0..0..0..0..1. .1..0..0..0..0. .1..1..0..0..1

Cf. A295120.

cp's OEIS Frontend

A295115 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A295116 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A295117 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A295118 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A295119 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A295114 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1's.

Views

Author

Keywords

Comments

Examples

Crossrefs