A069306 Number of 2 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, 18457556052, 44560482149, 107578520350, 259717522849, 627013566048, 1513744654945, 3654502875938

Offset: 2

Author

R. H. Hardin, Mar 14 2002

Keywords

• nonn
• easy

Links

• Indranil Ghosh, Table of n, a(n) for n = 2..2607
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,1).

Crossrefs

Cf. A069307 (3 X n), A069308 (4 X n), A069309 (5 X n), A069310 (6 X n), A069311 (7 X n), A069312 (8 X n), A069313 (9 X n), A069314 (10 X n), A069315 (11 X n), A069316 (12 X n), A069317 (13 X n), A069318 (14 X n), A069319 (15 X n), A069320 (16 X n).

Cf. A069294-A069305 (by columns).

Cf. A000129, A048624, A077985.

Programs

Mathematica

LinearRecurrence[{2, 1}, {5, 12}, 50] (* Paolo Xausa, Jul 19 2024 *)

Formula

G.f.: x^2(2x+5)/(1-2x-x^2). a(n) = A000129(n+1), as proved by Tomislav Doslic. - Ralf Stephan, Nov 16 2004

a(n) = 2*a(n-1)+a(n-2). [Philippe Deléham, Nov 20 2008]