A341905 a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.

3, 0, 2, 8, 10, 22, 48, 90, 182, 368, 730, 1462, 2928, 5850, 11702, 23408, 46810, 93622, 187248, 374490, 748982, 1497968, 2995930, 5991862, 11983728, 23967450, 47934902, 95869808, 191739610, 383479222, 766958448, 1533916890, 3067833782, 6135667568, 12271335130

Offset: 0

Author

Michael De Vlieger, Jun 04 2021

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..3322
• Evren Eyican Polatlı and Yüksel Soykan, On generalized third-order Jacobsthal numbers, Asian Res. J. of Math. (2021) Vol. 17, No. 2, 1-19, Article No. ARJOM.66022.
• Index entries for linear recurrences with constant coefficients, signature (1,1,2).

Crossrefs

Cf. A001045, A077947, A186575, A226308.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <2|1|1>>^n. <<3, 0, 2>>)[1,1]:
seq(a(n), n=0..34);  # Alois P. Heinz, Jun 04 2021

Mathematica

LinearRecurrence[{1, 1, 2}, {3, 0, 2}, 35] (* or *)
CoefficientList[Series[(-3 + 3 x + x^2)/(-1 + x + x^2 + 2 x^3), {x, 0, 34}], x]

Formula

G.f.: (-3 + 3*x + x^2)/(-1 + x + x^2 + 2*x^3).

a(n) = (10*2^(n-1) + 13*A049347(n) - 9*A079978(n+1) + 3)/7. - Greg Dresden, Jun 20 2021