A205493 Third row or column of table A205497.

1, 14, 109, 623, 2951, 12331, 47191, 169416, 579889, 1914226, 6144668, 19298724, 59579803, 181448918, 546629054, 1632497850, 4841448042, 14277423006, 41912838982, 122587133760, 357476552161, 1039922075888, 3019280091491, 8752184436454, 25337900299765

Offset: 0

Author

L. Edson Jeffery, Jan 28 2012

Keywords

• nonn

Comments

See A205497 regarding association of this sequence with generating functions for the rows of the tabular form of A050446.

Links

• L. E. Jeffery, Unit-primitive matrices

Crossrefs

Cf. A205497, A050446, A050447.

Programs

Python

# See program in A205497.

Formula

Conjecture 1. a(n) = M_{n,3} = M_{3,n}, where M = A205497.

Conjecture 2. Let w=2*cos(Pi/9). Then lim_{n->oo} a(n+1)/a(n) = w^3-2*w = spectral radius of the 4 X 4 unit-primitive matrix (see [Jeffery]) A_{9,3} = [0,0,0,1; 0,0,1,1; 0,1,1,1; 1,1,1,1].

Extensions

a(24) and changed title from Hugo Pfoertner, Jan 05 2020