A102102 Column 0 of triangular matrix A102101, which shifts upward to exclude the main diagonal under matrix fourth power.

1, 1, 15, 1000, 189035, 79278446, 63263422646, 86493299281972, 187766975052827491, 611024291011881918991, 2849262494779035461688236, 18362167739517547774072439880, 158759599858376078627687256207242

Offset

0,3

Comments

Analogous to A082161 and A082162, this describes the deterministic completely defined initially connected acyclic automata with 4 inputs and n transient unlabeled states (and a unique absorbing state) with a(0)=1.

Links

Table of n, a(n) for n=0..12.

Manosij Ghosh Dastidar and Michael Wallner, Asymptotics of relaxed k-ary trees, arXiv:2404.08415 [math.CO], 2024. See p. 1.4.

Prog

(PARI) {a(n)=local(A=matrix(1, 1), B); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=j, if(j==1, B[i, j]=(A^4)[i-1, 1], B[i, j]=(A^4)[i-1, j])); )); A=B); return(A[n+1, 1])}

Crossrefs

Cf. A102101, A082161, A082162.

Sequence in context: A067408 A274713 A229840 * A196569 A019282 A082158

Adjacent sequences: A102099 A102100 A102101 * A102103 A102104 A102105

Keyword

nonn

Author

Paul D. Hanna, Dec 29 2004

Status

approved