A069440 Half the number of n X 2 binary arrays with no path of adjacent 1's or adjacent 0's from top row to bottom row.

0, 2, 16, 88, 414, 1810, 7616, 31376, 127710, 516170, 2077552, 8341288, 33440190, 133941922, 536205056, 2145876128, 8586053694, 34350369050, 137416333936, 549701205496, 2198891419230, 8795774741170, 35183603690432, 140735633277488, 562945474867230

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (7,-13,3,4).

Formula

From Colin Barker, May 22 2012: (Start)

a(n) = 7*a(n-1) - 13*a(n-2) + 3*a(n-3) + 4*a(n-4).

G.f.: 2*x^2*(1+x+x^2)/((1-x)*(1-4*x)*(1-2*x-x^2)). (End)

a(n) = 2^(2*n-1) - A001333(n+1) + 1. - Sean A. Irvine, Aug 23 2024

Crossrefs

Cf. 2 X n A000079, n X 1 A000225, 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.

Sequence in context: A071893 A220505 A370192 * A000431 A281982 A207595

Adjacent sequences: A069437 A069438 A069439 * A069441 A069442 A069443

Keyword

nonn,easy

Author

R. H. Hardin, Mar 22 2002

Extensions

An incorrect recurrence was deleted by N. J. A. Sloane, Sep 13 2009

More terms from Sean A. Irvine, Aug 23 2024

Status

approved