A167910 a(n) = (4*3^n - 5*2^n + (-2)^n)/20.

0, 0, 1, 3, 13, 39, 133, 399, 1261, 3783, 11605, 34815, 105469, 316407, 953317, 2859951, 8596237, 25788711, 77431669, 232295007, 697147165, 2091441495, 6275373061, 18826119183, 56482551853, 169447655559, 508359743893, 1525079231679, 4575304803901, 13725914411703

Offset

0,4

Comments

a(n+1) - 3*a(n) = 0,1,0,4,0,16,0,64,.. is an "aerated" version of A000302.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,4,-12).

Formula

a(2*n+1) = 3*a(2*n).

a(n) = 3*a(n-1) + 4*a(n-2) - 12*a(n-3).

G.f.: x^2/((1-3*x)*(1-2*x)*(1+2*x)). - Philippe Deléham, Nov 15 2009

E.g.f.: (1/20)*(exp(-2*x) - 5*exp(2*x) + 4*exp(3*x)). - G. C. Greubel, Dec 04 2024

Mathematica

LinearRecurrence[{3, 4, -12}, {0, 0, 1}, 40] (* Harvey P. Dale, Mar 29 2015 *)

Prog

(Magma) [(4*3^n-5*2^n+(-2)^n)/20: n in [0..40] ]; // Vincenzo Librandi, Aug 06 2011
(Python)
def A167910(n): return (4*pow(3, n) - 5*pow(2, n) + pow(-2, n))//20
print([A167910(n) for n in range(41)]) # G. C. Greubel, Dec 04 2024

Crossrefs

Cf. A000302.

Sequence in context: A122504 A103277 A166897 * A147042 A018492 A227446

Adjacent sequences: A167907 A167908 A167909 * A167911 A167912 A167913

Keyword

nonn,easy

Author

Paul Curtz, Nov 15 2009

Extensions

Replaced definition by Lava formula of Nov 26 2009. Removed comments about unrelated sequences. - R. J. Mathar, Feb 27 2010

Status

approved