A347842 - OEIS

%I #9 Sep 16 2021 17:39:15

%S 1,6,148,14808,5942608,9546508128,61355108818240,1577381936031968640,

%T 162213856617581098030336,66726795842176170072717129216,

%U 109792555585903911536355551233758208,722612693482570097701467493432061846673408

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

%H Álvar Ibeas, <a href="/A347842/b347842.txt">Table of n, a(n) for n = 1..40</a>

%F 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.

%e a(3) = 148 = 1 * 1 + 21 * 2 + 105 * 1, counting:

%e the unrefined chain 0 < (F_4)^3;

%e 21 chains 0 < V < (F_4)^3, with dim(V) = 1; another

%e 21 chains 0 < V < (F_4)^3, with dim(V) = 2; and

%e 105 chains 0 < V_1 < V_2 < (F_4)^3.

%Y Cf. A289545, A347487, A036038.

%K nonn

%O 1,2

%A _Álvar Ibeas_, Sep 15 2021