A087438 a(n) = 3*2^(2*(n-1)) + 2^(n-2)*(n+1).

1, 4, 15, 56, 212, 816, 3184, 12544, 49728, 197888, 789248, 3151872, 12596224, 50360320, 201388032, 805437440, 3221504000, 12885491712, 51540852736, 206161051648, 824639225856, 3298546417664, 13194163650560, 52776608464896

Offset: 0

Author

Paul Barry, Sep 03 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A047926.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16).

Programs

Magma

[3*2^(2*(n-1))+2^(n-2)*(n+1): n in [0..25]]; // Vincenzo Librandi, May 21 2011

Mathematica

LinearRecurrence[{8,-20,16},{1,4,15},30] (* or *) CoefficientList[ Series[ (1-4x+3x^2)/((1-2x)^2(1-4x)),{x,0,30}],x] (* Harvey P. Dale, May 20 2011 *)

Formula

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

E.g.f.: (3*exp(4*x) + (1+2*x)*exp(2*x))/4.

a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3); a(0)=1, a(1)=4, a(2)=15. - Harvey P. Dale, May 20 2011