A083324 An alternating sum of decreasing powers.

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

Offset

0,2

Comments

Binomial transform of A083323.

Links

Table of n, a(n) for n=0..23.

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

Formula

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

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

Mathematica

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

Crossrefs

Equals 2 * A053154(n) + 1.

Sequence in context: A151111 A292278 A151112 * A238578 A151113 A151114

Adjacent sequences: A083321 A083322 A083323 * A083325 A083326 A083327

Keyword

easy,nonn

Author

Paul Barry, Apr 27 2003

Status

approved