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A322940 a(n) = [x^n] (4*x^2 + x - 1)/(2*x^2 + 3*x - 1).

%I A322940 #16 Apr 18 2023 15:27:29
%S A322940 1,2,4,16,56,200,712,2536,9032,32168,114568,408040,1453256,5175848,
%T A322940 18434056,65653864,233829704,832796840,2966049928,10563743464,
%U A322940 37623330248,133997477672,477239093512,1699712235880,6053614894664,21560269155752,76788037256584
%N A322940 a(n) = [x^n] (4*x^2 + x - 1)/(2*x^2 + 3*x - 1).
%H A322940 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3, 2).
%F A322940 a(n) = 3*a(n-1) + 2*a(n-2) for n >= 3.
%F A322940 a(n) = 2*A104934(n-1) for n >= 1.
%F A322940 a(n) = 4*A055099(n-2) for n >= 2.
%F A322940 INVERT(a) = A102865.
%F A322940 INVERTi(a) = A322939. (See the link 'Transforms' at the bottom of the page.)
%p A322940 a := proc(n) option remember; `if`(n < 3, [1, 2, 4][n+1], 3*a(n-1) + 2*a(n-2)) end:
%p A322940 seq(a(n), n=0..26);
%t A322940 Join[{1}, LinearRecurrence[{3, 2}, {2, 4}, 26]] (* _Jean-François Alcover_, Jul 13 2019 *)
%Y A322940 Row sums of A322941.
%Y A322940 Cf. A104934, A055099, A102865, A322939.
%K A322940 nonn
%O A322940 0,2
%A A322940 _Peter Luschny_, Jan 06 2019