A179608 a(n) = (7 + (-1)^n + 6*n)*2^(n-3).

1, 3, 10, 24, 64, 144, 352, 768, 1792, 3840, 8704, 18432, 40960, 86016, 188416, 393216, 851968, 1769472, 3801088, 7864320, 16777216, 34603008, 73400320, 150994944, 318767104, 654311424, 1375731712, 2818572288, 5905580032

Offset: 0

Author

Johannes W. Meijer, Jul 28 2010

Keywords

• easy
• nonn

Comments

This sequence belongs to a family of sequences with g.f. (1+x)/(1 - 2*x - (k+8)*x^2 - 2*k*x^3). Among the members of this family are several red king sequences, see A179596. For the sequence given above, which is not a red king sequence, k = -4.

Inverse binomial transform of A119916 (without the leading 0).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, 4, -8).

Programs

Magma

[(7+(-1)^n+6*n)*2^(n-3): n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

Formula

G.f.: (1+x)/(1 - 4*x^2 - 2*x + 8*x^3).

a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3) with a(1)=1, a(2)=3 and a(3)=10.

a(n) = (7 + (-1)^n + 6*n)*2^(n-3).