A347842 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_4)^n.

1, 1, 6, 148, 14808, 5942608, 9546508128, 61355108818240, 1577381936031968640, 162213856617581098030336, 66726795842176170072717129216, 109792555585903911536355551233758208, 722612693482570097701467493432061846673408, 19023844570798442009810731239392846416136188284928

Offset: 0

Author

Álvar Ibeas, Sep 15 2021

Keywords

• nonn

Examples

			a(3) = 148 = 1 * 1 + 21 * 2 + 105 * 1, counting:
the unrefined chain 0 < (F_4)^3;
21 chains 0 < V < (F_4)^3, with dim(V) = 1; another
21 chains 0 < V < (F_4)^3, with dim(V) = 2; and
105 chains 0 < V_1 < V_2 < (F_4)^3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..58 (terms n = 1..40 from Álvar Ibeas)

Crossrefs

Cf. A289545, A347487, A036038, A381299.

Column k=4 of A381426.

Programs

Maple

b:= proc(o, u, t) option remember; `if`(u+o=0, 1, `if`(t=1,
      b(u+o, 0$2), 0)+add(4^(u+j-1)*b(o-j, u+j-1, 1), j=1..o))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..14);  # Alois P. Heinz, Feb 21 2025

Formula

a(n) = Sum_{L partition of n} A347487(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.

a(n) = Sum_{k=0..binomial(n,2)} 4^k * A381299(n,k). - Alois P. Heinz, Feb 21 2025

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 21 2025