A347845 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_8)^n.

1, 1, 10, 804, 518376, 2674194448, 110368339035808, 36440751353074277952, 96254339565438079064819328, 2033964285682509941820879401890048, 343839935881726495233403720783311789640192, 465006794599984581603302662503095770372066384585728

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..47 (terms n = 1..40 from Álvar Ibeas)

Formula

a(n) = Sum_{L partition of n} A347490(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

Example

a(3) = 804 = 1 * 1 + 73 * 2 + 657 * 1, counting:
the unrefined chain 0 < (F_8)^3;
73 chains 0 < V < (F_8)^3, with dim(V) = 1; another
73 chains 0 < V < (F_8)^3, with dim(V) = 2; and
657 chains 0 < V_1 < V_2 < (F_8)^3.

Crossrefs

Cf. A289545, A347490, A036038.

Column k=8 of A381426.

Sequence in context: A322918 A233170 A211913 * A006440 A054944 A272854

Adjacent sequences: A347842 A347843 A347844 * A347846 A347847 A347848

Keyword

nonn

Author

Álvar Ibeas, Sep 15 2021

Extensions

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

Status

approved