A078904 a(n) = 4a(n-1) + 3n with a(0) = 0.

0, 3, 18, 81, 336, 1359, 5454, 21837, 87372, 349515, 1398090, 5592393, 22369608, 89478471, 357913926, 1431655749, 5726623044, 22906492227, 91625968962, 366503875905, 1466015503680, 5864062014783, 23456248059198, 93824992236861

Offset: 0

Author

Benoit Cloitre, Dec 12 2002

Keywords

• nonn

Crossrefs

Max ( Fr(n, k) : 1<=k<=4^(n+1)-3) where Fr(x, y) is defined in A078903.

Programs

Maple

a:=n->sum (4^j-1,j=1..n): seq(a(n),n=0..23); # Zerinvary Lajos, Jun 27 2007

Mathematica

s=0;lst={};Do[s+=2^n-1;AppendTo[lst, s], {n, 0, 6!, 2}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)

PARI

a(n)=(1/3)*(4^(n+1)-3*n-4)

Python

def A078904(n): return ((1<<(n+1<<1))-4)//3-n # Chai Wah Wu, Nov 12 2024

Sage

[gaussian_binomial(n,1,4)-n for n in range(1,25)] # Zerinvary Lajos, May 29 2009

Formula

G.f.: A(x) = -3x/(4x^3 - 9x^2 + 6x - 1).

a(n) = (1/3)*(4^(n+1) - 3*n - 4).

a(n) = 3*A014825(n). - Zerinvary Lajos, Jun 27 2007

Extensions

Additional formulas from Ralf Stephan, Dec 19 2002