A186575 -id:A186575 - cp's OEIS frontend

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

Michael De Vlieger, Jun 04 2021

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).

Cf. A001045, A077947, A186575, A226308.

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

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]

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

A331890 a(n) = -a(n-1) - a(n-2) + 2*a(n-3) with a(0)=3, a(1)=-1, a(2)=-1.

Original entry on oeis.org

3, -1, -1, 8, -9, -1, 26, -43, 15, 80, -181, 131, 210, -703, 755, 368, -2529, 3671, -406, -8323, 16071, -8560, -24157, 64859, -57822, -55351, 242891, -303184, -50409, 839375, -1395334, 455141, 2618943, -5864752, 4156091, 6946547, -22832142, 24197777

Offset: 0

Wojciech Florek, Jan 30 2020

a(n) is the reflected sequence (cf. A074058) of the generalized tribonacci sequence b(n) with b(0) = 3 and b(n) = A186575(n-1) for n > 0.

Mario Catalani, Polymatrix and Generalized Polynacci Numbers, arXiv:math/0210201 [math.CO], 2002.
Index entries for linear recurrences with constant coefficients, signature (-1,-1,2).

Cf. A074058, A186575.

a:=[3,-1,-1]; [n le 3 select a[n] else -Self(n-1)-Self(n-2)+2*Self(n-3):n in [1..30]]; // Marius A. Burtea, Feb 02 2020

LinearRecurrence[{-1,-1,2},{3,-1,-1},38] (* Stefano Spezia, Jan 31 2020 *)

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

a(n) = 3*A077975(n)+2*A077975(n-1)+A077975(n-2). - R. J. Mathar, Feb 28 2020

Definition clarified by N. J. A. Sloane, Apr 23 2020

cp's OEIS Frontend

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

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