A371843 a(n) = 5*Fibonacci(n) + (-1)^n.

1, 4, 6, 9, 16, 24, 41, 64, 106, 169, 276, 444, 721, 1164, 1886, 3049, 4936, 7984, 12921, 20904, 33826, 54729, 88556, 143284, 231841, 375124, 606966, 982089, 1589056, 2571144, 4160201, 6731344, 10891546, 17622889, 28514436, 46137324, 74651761, 120789084, 195440846

Offset: 0

Author

Paul Curtz, Apr 08 2024

Keywords

• nonn
• easy

Examples

			a(3) = 2*4 + 1 = 9. Also a(3) = -1 + 10*1 = 9.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Crossrefs

Cf. A000045, A022088, A033999, A097133.

Programs

Mathematica

LinearRecurrence[{0, 2, 1}, {1, 4, 6}, 50] (* Amiram Eldar, Apr 11 2024 *)

Formula

a(n) = a(n-2) + A022088(n-1).

a(n) = 2*a(n-2) + a(n-3).

a(n) = A022088(n) + A033999(n).

a(n) = - a(n-3) + 10*A000045(n-1) for n >= 3.

G.f.: (1+2*x)^2/((1+x)*(1-x-x^2)). - Joerg Arndt, Apr 13 2024