cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A094862 Same as A094858, except that we fix X = 123412341234...

Original entry on oeis.org

1, 2, 3, 4, 7, 10, 19, 28, 51
Offset: 1

Views

Author

Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004

Keywords

A094860 Same as A094858, except that we fix X = 121212...12(1).

Original entry on oeis.org

1, 2, 2, 3, 4, 6, 7, 10, 14, 20, 26, 36, 51, 70, 96, 141
Offset: 1

Views

Author

Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004

Keywords

A094861 Same as A094858, except that we fix X = 123123123...

Original entry on oeis.org

1, 2, 3, 4, 6, 10, 14, 24, 36, 58
Offset: 1

Views

Author

Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004

Keywords

Crossrefs

Cf. A094858.

A094291 a(n) = maximal value of C(i, j) * C(n-j, n-i) for 0 <= j <= i <= n.

Original entry on oeis.org

1, 2, 4, 9, 18, 40, 100, 225, 525, 1225, 3136, 7056, 17640, 44100, 108900, 261360, 637065, 1656369, 4008004, 10020010, 25050025, 64128064, 155739584, 393853824, 1012766976, 2538950544, 6347376360, 15868440900, 41408180100, 102252852900
Offset: 1

Views

Author

Hugo van der Sanden, Jun 15 2004

Keywords

Comments

This is the number of longest common subsequences between two binary strings of the form 00...011...1.
This is a lower bound for A094837, equivalent to choosing first string (x "a"s followed by (n-x) "b"s) and second string (y "a"s followed by (n-y) "b"s).

Examples

			a(3) is maximal with x=1, y=2, giving a(3) = C(2,1) * C(3-1,3-2). This is equivalent to the number of instances of length-2 common subsequences between "aab" and "abb".

Crossrefs

Cf. A094858-A094862, A094837, A094824, A094349, A094350.

A094859 Maximal number of longest common subsequences between any two ternary strings of length n (Version 2).

Original entry on oeis.org

1, 2, 3, 4, 6, 10
Offset: 1

Views

Author

Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004

Keywords

Comments

Same as A094858 but now we can use an alphabet of size 3.

A094863 Maximal number of longest common subsequences between any two strings of length n (Version 2).

Original entry on oeis.org

1, 2, 3, 4, 7, 10, 19, 28
Offset: 1

Views

Author

Guenter Stertenbrink (Sterten(AT)aol.com), Jun 14 2004

Keywords

Comments

Same as A094858 (which has much more information about the problem), except that we now we allow an arbitrary alphabet.
For even n it seems that the maximum is attained for X = 123412341234..., Y = 432143214321..., giving values : (conjectured) maximum number of maximum-length-common-subsequences of 2 strings of length 2*n over an arbitrary (infinite) alphabet f(2*n) = 2,4,10,28,78,220,624,1780,5100,14668,.. Note that (3*f(2*n)-f(2*n+2))/2 gives 1,1,1,3,7,18,46,120,316,841,2257,6103,16611,45475,125139,.. which is A026107. Is there an explanation for this?

Crossrefs

Cf. A026107, A094858.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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