login
4^n-2^n-2.
2

%I #8 Jul 28 2015 16:39:50

%S 0,10,54,238,990,4030,16254,65278,261630,1047550,4192254,16773118,

%T 67100670,268419070,1073709054,4294901758,17179738110,68719214590,

%U 274877382654,1099510579198,4398044413950,17592181850110,70368735789054,281474959933438,1125899873288190

%N 4^n-2^n-2.

%C a(n) is also the number whose binary representation is the concatenation of n-1 1's, 0, n-1 1's and 0 (See example). [From _Omar E. Pol_, Mar 16 2010]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -14, 8).

%F a(n)= 7*a(n-1) -14*a(n-2) +8*a(n-3) = 2*A129868(n-1). G.f.: 2*x^2*(-5+8*x)/((x-1) * (2*x-1) * (4*x-1)). [From _R. J. Mathar_, Feb 14 2010]

%F a(n) = 2*(A006516(n)-1) [From _Omar E. Pol_, Mar 16 2010]

%e Contribution from _Omar E. Pol_, Mar 16 2010: (Start)

%e n ...... a(n) written in base 2 ..... a(n)

%e 1 ................ 0 ................ 0

%e 2 ............... 1010 .............. 10

%e 3 .............. 110110 ............. 54

%e 4 ............. 11101110 ............ 238

%e 5 ............ 1111011110 ........... 990

%e 6 ........... 111110111110 .......... 4030

%e 7 .......... 11111101111110 ......... 16254

%e 8 ......... 1111111011111110 ........ 65278

%e 9 ........ 111111110111111110 ....... 261630

%e 10 ...... 11111111101111111110 ...... 1047550

%e (End)

%Y Cf. A170926.

%Y Cf. A006516, A138148, A173521. [From _Omar E. Pol_, Mar 16 2010]

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Feb 13 2010