A078904 - OEIS

%I #20 Nov 13 2024 17:16:05

%S 0,3,18,81,336,1359,5454,21837,87372,349515,1398090,5592393,22369608,

%T 89478471,357913926,1431655749,5726623044,22906492227,91625968962,

%U 366503875905,1466015503680,5864062014783,23456248059198,93824992236861

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

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

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

%F a(n) = 3*A014825(n). - _Zerinvary Lajos_, Jun 27 2007

%p a:=n->sum (4^j-1,j=1..n): seq(a(n),n=0..23); # _Zerinvary Lajos_, Jun 27 2007

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

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

%o (Sage) [gaussian_binomial(n,1,4)-n for n in range(1,25)] # _Zerinvary Lajos_, May 29 2009

%o (Python)

%o def A078904(n): return ((1<<(n+1<<1))-4)//3-n # _Chai Wah Wu_, Nov 12 2024

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

%K nonn

%O 0,2

%A _Benoit Cloitre_, Dec 12 2002

%E Additional formulas from _Ralf Stephan_, Dec 19 2002