%I A121544
%S A121544 6,114,1896,30624,491136,7862784,125822976,2013241344,32212156416,
%T A121544 515395682304
%N A121544 Sum of all proper base 4 numbers with n digits (those not beginning with 
               0).
%C A121544 Sum of the first 3*(4^(n-1)) integers starting with 4^(n-1). Sum of the 
               integers from 4^(n-1) to (4^n)-1. First differences of A026337 4^n*(4^n-1)/
               2. cf. A007090 Numbers in base 4. cf. A010036 = Sum of all proper 
               binary numbers with n digits (i.e. those not beginning with 0) = 
               Sum of 2^n, ..., 2^(n+1) - 1 = 3*2^(2*n-3)-2^(n-2). cf. A101291 Sum 
               of all numbers with n digits [base 10]. cf. A026121 3^n*(3^n-1)/2.
%F A121544 a(n) = (4^(n-1) + 4^n - 1) * 3 * (4^(n-1))/2.
%e A121544 a(1) = 6 = 1 + 2 + 3.
%e A121544 a(2) = 114 = 10_4 + 11_4 + 12_4 + 13_4 + 20_4 + 21_4 + 22_4 + 23_4 + 
               30_4 + 31_4 + 32_4 + 33_4 = (4+5+6+7+8+9+10+11+12+13+14+15)_10.
%Y A121544 Cf. A007090, A010036, A026121, A026337, A101291.
%Y A121544 Sequence in context: A066931 A051228 A059116 this_sequence A003425 A052465 
               A113015
%Y A121544 Adjacent sequences: A121541 A121542 A121543 this_sequence A121545 A121546 
               A121547
%K A121544 easy,nonn,base
%O A121544 1,1
%A A121544 Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 08 2006