A069308 -id:A069308 - cp's OEIS frontend

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

R. H. Hardin, Mar 14 2002

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).

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.

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

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]

A069320 Number of 16 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

1431655765, 65745948074080, 3162178031998196717, 156408973727702579374000

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 8 X n A069312, 9 X n A069313, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, by columns A069294-A069305.

A069309 Number of 5 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

341, 7556, 172143, 3958316, 91369811, 2112274668, 48861110849, 1130534931080, 26160665637805, 605385196535596, 14009490587031167, 324202249915245972, 7502586497280931603, 173622714928362682332, 4017929413014868925321, 92981844689395440980600

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 6 X n A069310, 7 X n A069311, 8 X n A069312, 9 X n A069313, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

A069310 Number of 6 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

1365, 60920, 2816409, 132103824, 6238756831, 295545642334, 14020698615685, 665580139683936, 31605577678427531, 1501028805154667736, 71292415421456529651, 3386189554819795682250, 160836875185955529578497, 7639466332037337857340948, 362862300943189672121948117

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 7 X n A069311, 8 X n A069312, 9 X n A069313, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069311 Number of 7 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

5461, 488860, 45550691, 4324832140, 414680716163, 39959490285500, 3860368291738151, 373423075547578456, 36146216722785667861, 3500044399151834410528, 338969996144009158522891, 32831359005580196869725148, 3180073668375520890944381755

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 8 X n A069312, 9 X n A069313, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069312 Number of 8 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

21845, 3915640, 732630205, 140129819328, 27139451744971, 5292500285670344, 1036037626157286045, 203239076083010593472, 39916149930281967457205, 7844661838902748923237822, 1542263634548542336151173999, 303271759994928192091591236664

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 9 X n A069313, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069313 Number of 9 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

87381, 31340216, 11751896403, 4514892704132, 1760130435695027, 692128295029569712, 273552889555043981667, 108443838410200501279708, 43066986985849138740694549, 17121637307123834033940314568, 6811155547203848959429866325465, 2710567644648890574598792001139520

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 8 X n A069312, 10 X n A069314, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069314 10 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

349525, 250769592, 188262802525, 145019645494844, 113542011614104379, 89798972465698310480, 71469066339273464672861, 57104283197019200756790188, 45738751568329997358178054329, 36691638903540665604692077389476, 29462439537258441022480797977381647

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 8 X n A069312, 9 X n A069313, 11 X n A069315, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069315 Number of 11 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

1398101, 2006308480, 3014016321451, 4650208682728432, 7301005843380595779, 11592951743199556912876, 18543498700760853810422275, 29803331617203085845704313992, 48049989770896486757102805620329, 77626289171582272584203485766947172

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..200

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 8 X n A069312, 9 X n A069313, 10 X n A069314, 12 X n A069316, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

A069316 Number of 12 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

Original entry on oeis.org

5592405, 16050948896, 48238373155229, 148975517675350528, 468579743984737735163, 1491945234246315077238684, 4789484633305049073669332993, 15460814292574112201614850454092, 50096394975413699108192666406325657, 162737494025555699251138581672556381200

Offset: 2

R. H. Hardin, Mar 14 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 2..100

Cf. 2 X n A069306, 3 X n A069307, 4 X n A069308, 5 X n A069309, 6 X n A069310, 7 X n A069311, 8 X n A069312, 9 X n A069313, 10 X n A069314, 11 X n A069315, 13 X n A069317, 14 X n A069318, 15 X n A069319, 16 X n A069320, by columns A069294-A069305.

More terms from Sean A. Irvine, Apr 26 2024

cp's OEIS Frontend

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.

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A069320 Number of 16 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069309 Number of 5 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069310 Number of 6 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069311 Number of 7 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069312 Number of 8 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069313 Number of 9 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069314 10 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069315 Number of 11 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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A069316 Number of 12 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.

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