A334293 First quadrisection of Padovan sequence.

1, 0, 2, 5, 16, 49, 151, 465, 1432, 4410, 13581, 41824, 128801, 396655, 1221537, 3761840, 11584946, 35676949, 109870576, 338356945, 1042002567, 3208946545, 9882257736, 30433357674, 93722435101, 288627200960, 888855064897, 2737314167775, 8429820731201, 25960439030624

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,1).

Formula

a(n) = A000931(4n).

a(n) = A099529(2n).

a(n) = Sum_{k=0..n} binomial(2*n-k-1, 2*k-1).

a(n) = 2*a(n-1)+3*a(n-2)+a(n-3), a(0)=1, a(1)=0, a(2)=2 for n>=3.

G.f.: (1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3). - Colin Barker, Apr 27 2020

Example

For n=3, a(3) = 2*a(2) + 3*a(1) + a(0) = 2*2 + 3*0 + 1 = 5.

Prog

(PARI) Vec((1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3) + O(x^30)) \\ Colin Barker, Apr 27 2020

Crossrefs

Quadrisection of A000931.

Bisection (even part) of A099529.

Cf. A099098, A091140.

Sequence in context: A210696 A005497 A148381 * A278274 A148382 A148383

Adjacent sequences: A334290 A334291 A334292 * A334294 A334295 A334296

Keyword

nonn,easy

Author

Oboifeng Dira, Apr 21 2020

Status

approved