A083324 a(n) = 4^n - 3^n + 2^n.

1, 3, 11, 45, 191, 813, 3431, 14325, 59231, 242973, 990551, 4019205, 16249871, 65522733, 263668871, 1059425685, 4251986111, 17050860093, 68332318391, 273716169765, 1096025891951, 4387588255053, 17560809179111, 70274609387445, 281192563951391, 1125052651787613

Offset: 0

Author

Paul Barry, Apr 27 2003

Keywords

• nonn
• easy

Comments

An alternating sum of decreasing powers.

Binomial transform of A083323.

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

Crossrefs

Cf. A053154, A083323.

Programs

Mathematica

Table[4^n-3^n+2^n,{n,0,23}] (* Geoffrey Critzer, Dec 01 2013 *)

Formula

a(n) = 2 * A053154(n) + 1.

G.f.: (1-6*x+10*x^2)/((1-2*x)*(1-3*x)*(1-4*x)).

E.g.f.: exp(4*x) - exp(3*x) + exp(2*x).

a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3). - Geoffrey Critzer, Dec 01 2013