A016269 -id:A016269 - cp's OEIS frontend

A069407 Half the number of n X 7 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

63, 6069, 476389, 33438451, 2230830597

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069408 Half the number of n X 8 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

127, 26335, 4461489, 669776139, 94819936513

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069409 Half the number of n X 9 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

255, 111645, 40306317, 12817737731, 3816886269599

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069410 Half the number of n X 10 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

511, 465751, 354713977, 237180629275

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069411 Half the number of n X 11 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

1023, 1921029, 3060942133, 4277806868563

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069412 Half the number of n X 12 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

2047, 7859215, 26020259201, 75628309151275

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069413 Half the number of n X 13 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

4095, 31964205, 218626028573, 1315968756706339

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069414 Half the number of n X 14 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

8191, 129442951, 1820140085705, 22606389934281147

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A069415 Half the number of n X 15 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

Original entry on oeis.org

16383, 522538389, 15043088032837, 384286142618740851

Offset: 1

R. H. Hardin, Mar 22 2002

nonn

Cf. 1 X n A000225, 2 X n A016269, 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.

A084880 Number of (k,m,n)-multiantichains of multisets with k=3 and m=3.

Original entry on oeis.org

1, 3, 28, 701, 28156, 1105553, 38746288, 1242925421, 37586964436, 1093785614153, 31039025026648, 866337233127941, 23916052195646716, 655400382364459553, 17872830907936220608, 485794685997062639261, 13175148372787020760996

Offset: 0

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

nonn

By a (k,m,n)-multiantichain of multisets we mean an m-multiantichain of k-bounded multisets on an n-set. The elements of a multiantichain could have the multiplicities greater than 1. A multiset is called k-bounded if every its element has the multiplicity not greater than k-1.

Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (77,-2277,32895,-242514,854388,-1102248).

Cf. A016269, A047707, A051112-A051118, A084869-A084883.

[(27^n - 6*18^n + 6*14^n + 9*9^n - 18*6^n + 14*3^n)/6: n in [0..50]]; // G. C. Greubel, Oct 08 2017

LinearRecurrence[{77,-2277,32895,-242514,854388,-1102248},{1,3,28,701, 28156,1105553},20] (* Harvey P. Dale, Apr 08 2015 *)
Table[(27^n - 6*18^n + 6*14^n + 9*9^n - 18*6^n + 14*3^n)/6, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)

for(n=0,50, print1((27^n - 6*18^n + 6*14^n + 9*9^n - 18*6^n + 14*3^n)/6, ", ")) \\ G. C. Greubel, Oct 08 2017

a(n) = (27^n - 6*18^n + 6*14^n + 9*9^n - 18*6^n + 14*3^n)/6.
G.f.: (1 - 74*x + 2074*x^2 - 27519*x^3 + 181764*x^4 - 514188*x^5) / ( (18*x-1)*(9*x-1)*(6*x-1)*(3*x-1)*(14*x-1)*(27*x-1) ). - R. J. Mathar, Jul 08 2011
a(0)=1, a(1)=3, a(2)=28, a(3)=701, a(4)=28156, a(5)=1105553, a(n) = 77*a(n-1) - 2277*a(n-2) + 32895*a(n-3) - 242514*a(n-4) + 854388*a(n-5) - 1102248*a(n-6). - Harvey P. Dale, Apr 08 2015

cp's OEIS Frontend

A069407 Half the number of n X 7 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069408 Half the number of n X 8 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069409 Half the number of n X 9 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069410 Half the number of n X 10 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069411 Half the number of n X 11 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069412 Half the number of n X 12 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069413 Half the number of n X 13 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069414 Half the number of n X 14 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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A069415 Half the number of n X 15 binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.

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Author

Keywords

Crossrefs

A084880 Number of (k,m,n)-multiantichains of multisets with k=3 and m=3.

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