A034182 -id:A034182 - cp's OEIS frontend

A069419 Number of 5 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

1, 97, 5149, 217253, 8168645, 287275073, 9681281781

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069420 Number of 6 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 237, 28159, 2575297, 206458895

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069421 Number of 7 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 575, 151331, 29682643

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069422 Number of 8 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 1391, 806463, 337104939

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069423 Number of n X 3 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 19, 147, 907, 5149, 28159, 151331, 806463, 4280141, 22670199, 119955523, 634412111, 3354416225, 17734138519, 93751306327, 495600489243, 2619870168133, 13849199313235, 73209594712831, 386999645945759, 2045750897807901, 10814208630415211, 57165847109895879

Offset: 1

R. H. Hardin, Mar 22 2002

Index entries for linear recurrences with constant coefficients, signature (11,-41,64,-35,-13,25,-12,2).

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

a(n) = A069378(n) - 2 * A069403(n). - Sean A. Irvine, Aug 23 2024

G.f.: x*(2*x^7-10*x^6+23*x^5-18*x^4-5*x^3+21*x^2-8*x-1) / ((x-1)*(x^2-3*x+1)*(2*x^5-4*x^4+x^3+9*x^2-7*x+1)). - Alois P. Heinz, Aug 23 2024

More terms from Sean A. Irvine, Aug 23 2024

A069424 Number of n X 4 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 65, 1231, 17339, 217253, 2575297, 29682643, 337104939, 3798244149, 42611591165, 476921965419, 5330934738199, 59545502975241, 664849480893793, 7421696282496891, 82838232515999423, 924548372982432205, 10318403957821437753, 115156011527942405255

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

a(n) = A069379(n) - 2 * A069404(n). - Sean A. Irvine, Aug 23 2024

More terms from Sean A. Irvine, Aug 23 2024

A069425 Number of n X 5 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 211, 9539, 300651, 8168645, 206458895, 5022868187, 119647195507, 2816023729437, 65818825735031, 1532136293558119, 35579894275049831, 825082170362304285, 19117256012937548815, 442728846445605819023, 10249950234312030878755, 237262687880593853560805

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

a(n) = A069380(n) - 2 * A069405(n). - Sean A. Irvine, Aug 23 2024

More terms from Sean A. Irvine, Aug 23 2024

A069426 Number of n X 6 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 665, 70679, 4927163, 287275073

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A069427 Number of n X 7 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1, 2059, 509019, 77892523, 9681281781

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 2 X n A001047, n X 2 A034182, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

A098894 Values of k such that {s(1),...,s(k)} is a palindrome, where {s(1),s(2),...} is the fixed point of the substitutions 0->1 and 1->110.

Original entry on oeis.org

1, 2, 5, 8, 15, 22, 39, 56, 97, 138, 237, 336, 575, 814, 1391, 1968, 3361, 4754, 8117, 11480, 19599, 27718, 47319, 66920, 114241, 161562, 275805, 390048, 665855, 941662, 1607519, 2273376, 3880897, 5488418, 9369317

Offset: 1

John W. Layman, Nov 04 2004

nonn

Superseeker suggests: (1) o.g.f. (1+x+x^2+x^3)/(1+2x-2x^2-x^3+x^4+x^5), (2) terms of odd index {1,5,15,39,...} give A034182 and (3) {a(n)+2} gives A082766, except for several initial terms.

Conjecture: partial sums of A152113. - Sean A. Irvine, Jul 14 2022

			Start with 1 and iterate the substitutions 0->1, 1->110 to get 1, 110, 1101101, 11011011101101110, 11011011101101110110110111011011101101101,... The initial terms from the beginning to the single quotes form palindromes: 1'1'011'011'1011011'1011011',..., of lengths 1,2,5,8,15,22,...

Cf. A034182, A082766.

cp's OEIS Frontend

A069419 Number of 5 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069420 Number of 6 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069421 Number of 7 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069422 Number of 8 X n binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069423 Number of n X 3 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069424 Number of n X 4 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069425 Number of n X 5 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069426 Number of n X 6 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A069427 Number of n X 7 binary arrays with a path of adjacent 1's and no path of adjacent 0's from top row to bottom row.

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A098894 Values of k such that {s(1),...,s(k)} is a palindrome, where {s(1),s(2),...} is the fixed point of the substitutions 0->1 and 1->110.

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