OFFSET
0,4
COMMENTS
In characteristic zero the analogous numbers are A001405.
LINKS
K. Coulembier, P. Etingof, V. Ostrik, and D. Tubbenhauer, Fractal behavior of tensor powers of the two dimensional space in prime characteristic, arXiv:2405.16786 [math.RT], 2024.
M. Larsen, Bounds for SL2-indecomposables in tensor powers of the natural representation in characteristic 2, arXiv:2405.16015 [math.RT], 2024.
Daniel Tubbenhauer, GitHub page
FORMULA
a(0) = a(1) = 1, and for n>1: a(2n-1) = a(2n) = Sum_{k=0..n-1} binomial(n-1,k)*2^(n-1-k)*a(k).
a(n) ~ h(n)*n^(t)*2^n for t=1/2log_2(3/2)-1 approx. -0.707 and h(n) a bounded function. The constant t is A153460 - 2.
MATHEMATICA
a[0|1] = 1; a[n_] := a[n] = With[{m = Ceiling[n/2]}, Sum[Binomial[m-1, k] 2^(m-1-k) a[k], {k, 0, m-1}]]; Table[a[n], {n, 0, 40}]
PROG
(PARI) a(n) = if (n<=1, 1, my(m=ceil(n/2)); sum(k=0, m-1, binomial(m-1, k)*2^(m-1-k)*a(k))); \\ Michel Marcus, Jun 01 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Tubbenhauer, Jun 01 2024
STATUS
approved