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

%I #16 Apr 18 2023 15:27:29

%S 1,2,4,16,56,200,712,2536,9032,32168,114568,408040,1453256,5175848,

%T 18434056,65653864,233829704,832796840,2966049928,10563743464,

%U 37623330248,133997477672,477239093512,1699712235880,6053614894664,21560269155752,76788037256584

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3, 2).

%F a(n) = 3*a(n-1) + 2*a(n-2) for n >= 3.

%F a(n) = 2*A104934(n-1) for n >= 1.

%F a(n) = 4*A055099(n-2) for n >= 2.

%F INVERT(a) = A102865.

%F INVERTi(a) = A322939. (See the link 'Transforms' at the bottom of the page.)

%p a := proc(n) option remember; `if`(n < 3, [1, 2, 4][n+1], 3*a(n-1) + 2*a(n-2)) end:

%p seq(a(n), n=0..26);

%t Join[{1}, LinearRecurrence[{3, 2}, {2, 4}, 26]] (* _Jean-François Alcover_, Jul 13 2019 *)

%Y Row sums of A322941.

%Y Cf. A104934, A055099, A102865, A322939.

%K nonn

%O 0,2

%A _Peter Luschny_, Jan 06 2019

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)