A347846 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_9)^n.

1, 1, 11, 1093, 979163, 7895396653, 572984959186643, 374244678702477629605, 2199939020346263706461674955, 116387990444553949414146511586296381, 55417662962428710787068813831544886356769891, 237482030708312867514661156730660313316831290472695733

Offset: 0

Author

Álvar Ibeas, Sep 15 2021

Keywords

• nonn

Examples

			a(3) = 1093 = 1 * 1 + 91 * 2 + 910 * 1, counting:
the unrefined chain 0 < (F_9)^3;
91 chains 0 < V < (F_9)^3, with dim(V) = 1; another
91 chains 0 < V < (F_9)^3, with dim(V) = 2; and
910 chains 0 < V_1 < V_2 < (F_9)^3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..46 (terms n = 1..40 from Álvar Ibeas)

Crossrefs

Cf. A289545, A347491, A036038, A381299.

Column k=9 of A381426.

Formula

a(n) = Sum_{L partition of n} A347491(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 25 2025