A336452 Triangle read by rows, the Riordan square of the number of achiral m-color cyclic compositions of n (A308747). T(n,k) for 1 <= k <= n.

1, 3, 3, 6, 15, 9, 13, 49, 63, 27, 23, 137, 276, 243, 81, 44, 338, 969, 1323, 891, 243, 73, 782, 2950, 5589, 5778, 3159, 729, 131, 1695, 8161, 20097, 28485, 23733, 10935, 2187, 210, 3545, 20966, 64557, 117801, 133569, 93312, 37179, 6561

Offset

1,2

Comments

See the link and A321620 for more information about the Riordan square transform.

Links

Table of n, a(n) for n=1..45.

Petros Hadjicostas, Generalized colored circular palindromic compositions, Moscow Journal of Combinatorics and Number Theory, 9(2) (2020), 173-186.

Peter Luschny, The Riordan Square Transform, 2018.

Example

[1] [   1]
[2] [   3,    3]
[3] [   6,   15,     9]
[4] [  13,   49,    63,    27]
[5] [  23,  137,   276,   243,     81]
[6] [  44,  338,   969,  1323,    891,    243]
[7] [  73,  782,  2950,  5589,   5778,   3159,   729]
[8] [ 131, 1695,  8161, 20097,  28485,  23733, 10935,  2187]
[9] [ 210, 3545, 20966, 64557, 117801, 133569, 93312, 37179, 6561]

Prog

(SageMath) # using riordan_square_array from A321620, A308747.
riordan_square_array([1, 3, 6, 13, 23, 44, 73, 131, 210])

Crossrefs

Cf. A308747, A321620.

Sequence in context: A110523 A145597 A143418 * A092370 A245796 A345908

Adjacent sequences: A336449 A336450 A336451 * A336453 A336454 A336455

Keyword

nonn,tabl

Author

Peter Luschny, Aug 09 2020

Status

approved