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 1-3 of 3 results.

A281442 Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Kauffman monoid K_n.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 4, 0, 1, 0, 8, 0, 6, 0, 1, 0, 0, 22, 0, 8, 0, 1, 0, 42, 0, 40, 0, 10, 0, 1, 0, 0, 140, 0, 62, 0, 12, 0, 1, 0, 262, 0, 288, 0, 88, 0, 14, 0, 1, 0, 0, 992, 0, 492, 0, 118, 0, 16, 0, 1
Offset: 0

Views

Author

James East, Oct 05 2017

Keywords

Comments

Values were computed using the Semigroups package for GAP.
T(n,r) is also the number of idempotent basis elements of rank r in the Temperley-Lieb algebra of degree n in the generic case (when the twisting parameter is not an m-th root of unity for any m <= n).

Links

Crossrefs

Cf. A281438 (row sums), A281441, A289620.

Formula

T(2n-1,1) = A005315(n). Empirical: T(2n,2) = A077056(n); T(n+2,n-2) = 2*A028875(n) for n>2. - Andrey Zabolotskiy, Oct 19 2017

A281441 Triangle read by rows: T(n,r), 0 <= r <= n, is the number of idempotents of rank r in the Jones monoid J_n.

Original entry on oeis.org

1, 0, 1, 1, 0, 1, 0, 4, 0, 1, 4, 0, 7, 0, 1, 0, 25, 0, 10, 0, 1, 25, 0, 57, 0, 13, 0, 1, 0, 196, 0, 98, 0, 16, 0, 1, 196, 0, 522, 0, 148, 0, 19, 0, 1, 0, 1764, 0, 1006, 0, 207, 0, 22, 0, 1, 1764, 0, 5206, 0, 1673, 0, 275, 0, 25, 0, 1
Offset: 0

Views

Author

James East, Oct 05 2017

Keywords

Comments

Values were computed using the Semigroups package for GAP.

Links

Crossrefs

Cf. A225798 (row sums), A281442, A289620, A001246, A016777.

Formula

T(2n,0) = T(2n+1,1) = A001246(n). T(2n+2,2n) = A016777(n). - Andrey Zabolotskiy, Oct 19 2017

A286867 Number of idempotents in the twisted planar partition monoid PP_n^tau.

Original entry on oeis.org

1, 1, 6, 44, 362, 3226, 30488, 301460, 3090020, 32618046, 345515557
Offset: 0

Views

Author

James East, Oct 05 2017

Keywords

Comments

Values were computed using the Semigroups package for GAP.

Links

Crossrefs

Cf. A225797, A289620.
Showing 1-3 of 3 results.

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

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