A168615 Inverse binomial transform of A169609, or of A144437 preceded by 1.

1, 2, -2, 0, 6, -18, 36, -54, 54, 0, -162, 486, -972, 1458, -1458, 0, 4374, -13122, 26244, -39366, 39366, 0, -118098, 354294, -708588, 1062882, -1062882, 0, 3188646, -9565938, 19131876, -28697814, 28697814, 0, -86093442, 258280326, -516560652

Offset: 0

Author

Paul Curtz, Dec 01 2009

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3,-3).

Crossrefs

Cf. A169609, A144437, A000748, A057083, A057682.

Programs

Magma

[ n le 2 select n else n eq 3 select -2 else -3*Self(n-1)-3*Self(n-2): n in [1..37] ]; // Klaus Brockhaus, Dec 03 2009

Mathematica

Join[{1,2,-2}, LinearRecurrence[{-3, -3}, {0, 6}, 25]] (* G. C. Greubel, Jul 27 2016 *)
LinearRecurrence[{-3,-3},{1,2,-2},40] (* Harvey P. Dale, Jul 21 2024 *)

Formula

a(n) = -3*a(n-1) - 3*a(n-2) for n > 2; a(0) = 1, a(1) = 2, a(2) = -2.

a(n) = 2*A123877(n-1), n>0.

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

a(6*m + 3) = 0, m>=0. - G. C. Greubel, Jul 27 2016

Extensions

Edited and extended by Klaus Brockhaus, Dec 03 2009