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

1, 2, 4, 16, 56, 200, 712, 2536, 9032, 32168, 114568, 408040, 1453256, 5175848, 18434056, 65653864, 233829704, 832796840, 2966049928, 10563743464, 37623330248, 133997477672, 477239093512, 1699712235880, 6053614894664, 21560269155752, 76788037256584

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (3, 2).

Formula

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

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

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

INVERT(a) = A102865.

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

Maple

a := proc(n) option remember; `if`(n < 3, [1, 2, 4][n+1], 3*a(n-1) + 2*a(n-2)) end:
seq(a(n), n=0..26);

Mathematica

Join[{1}, LinearRecurrence[{3, 2}, {2, 4}, 26]] (* Jean-François Alcover, Jul 13 2019 *)

Prog

(PARI) a(n)=if(n, ([0, 1; 2, 3]^(n-1)*[2; 4])[1, 1], 1) \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Row sums of A322941.

Cf. A104934, A055099, A102865, A322939.

Sequence in context: A087972 A010362 A262164 * A306519 A001472 A053498

Adjacent sequences: A322937 A322938 A322939 * A322941 A322942 A322943

Keyword

nonn,easy

Author

Peter Luschny, Jan 06 2019

Status

approved