A084525 -id:A084525

Search: a084525 -id:a084525

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A084505

Partial sums of A084506.

+10
6

0, 1, 3, 5, 8, 11, 14, 17, 20, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

For n>=1, (a(n-1)+1,a(n)) = (1,1),(2,3),(4,5),(6,8),(9,11),(12,14),... gives the starting and ending offsets of the n-th site swap in the sequence A084501.

Note: this sequence is related to juggling with three objects. For a similar sequence related to (ordinary) permutations, see A084555.

LINKS

A. Karttunen, Table of n, a(n) for n = 0..32770

A. Karttunen, Scheme-program for computing this sequence

Index entries for sequences related to juggling

CROSSREFS

Differs from A084555 first time at the 130th term, where A084505(130) = 605, while A084555(130) = 604.

A084503(a(n)) = 7 for all n. However, this does not give the positions of all 7s in A084503 because the state sequences are not all indecomposable. Cf. A084515, A084525.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2003

EXTENSIONS

Added the b-file, moved the misplaced Mathematica code to A084555, where it belongs. - Antti Karttunen, Oct 24 2012

STATUS

approved

A084515

Partial sums of A084516.

+10
6

0, 1, 3, 6, 9, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 69, 74, 79, 84, 89, 94, 99, 104, 109, 114, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249, 254, 259, 264, 269

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

For n>=1, (a(n-1)+1,a(n)) = (1,1),(2,3),(4,6),(7,9),(10,12),... gives the starting and ending offsets of the n-th site swap in the sequence A084511. Gives also the positions of 7s (ground states) in A084513.

LINKS

Table of n, a(n) for n=0..59.

A. Karttunen, Scheme-program for computing this sequence

CROSSREFS

Differs from A084525 first time at the 18th term, where A084515(18) = 64, while A084525(18) = 65.

Cf. also A084505.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2003

STATUS

approved

A084526

The length of each successively larger, indecomposable, 'prime' 3-ball ground-state site swap given in A084521, i.e., the number of digits in each term of A084522.

+10
6

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..105.

A. Karttunen, Scheme-program for computing this sequence

CROSSREFS

Partial sums: A084525. Differs from A084516 first time at the 18th term, where A084516(18) = 4, while A084526(18) = 5. Cf. also A084506, A084520, A084528.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2003

STATUS

approved

A084520

a(0)=0, after which each n occurs A084526(n) times.

+10
5

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Also minimum i such that A084525(i) >= n. Tells that the n-th throw (n>=1) in A084521 belongs to the a(n)-th lexicographical solution A084522(a(n)).

LINKS

Table of n, a(n) for n=0..78.

A. Karttunen, Scheme-program for computing this sequence

CROSSREFS

Differs from A084510 first time at the 65th term, where A084510(65) = 19, while A084520(65) = 18. Cf. A084500.

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2003

STATUS

approved

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