A322783 a(n) = 1 - n + (2^(n+2) - (-1)^n)/3.

2, 3, 4, 9, 18, 39, 80, 165, 334, 675, 1356, 2721, 5450, 10911, 21832, 43677, 87366, 174747, 349508, 699033, 1398082, 2796183, 5592384, 11184789, 22369598, 44739219, 89478460, 178956945, 357913914, 715827855, 1431655736

Offset: 0

Author

Paul Curtz, Dec 26 2018

Keywords

• nonn
• easy

Comments

a(n) mod 10 = period 20: repeat [2, 3, 4, 9, 8, 9, 0, 5, 4, 5, 6, 1, 0, 1, 2, 7, 6, 7, 8, 3] = disordered [0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9].

Links

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

Crossrefs

Cf. A001045, A004442(n-2), A097073, A097074.

Programs

PARI

Vec((2 - 3*x - 3*x^2 + 6*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Dec 26 2018

Formula

a(n+1) - 2*(n) = -1, -2, 1, 0, 3, 2, 5, 4, ..., n >= 0.

a(n+1) - a(n) = A097074(n).

a(n+2) - 2*a(n+1) + a(n) = A097073(n+1).

From Colin Barker, Dec 26 2018: (Start)

G.f.: (2 - 3*x - 3*x^2 + 6*x^3) / ((1 - x)^2*(1 + x)*(1 - 2*x)).

a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4) for n > 3.

(End)