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A121544 Sum of all proper base 4 numbers with n digits (those not beginning with 0). 1

%I

%S 6,114,1896,30624,491136,7862784,125822976,2013241344,32212156416,

%T 515395682304,8246335635456,131941389041664,2111062300164096,

%U 33776997104615424,540431954881806336,8646911282940739584,138350580546379186176,2213609288819376390144

%N Sum of all proper base 4 numbers with n digits (those not beginning with 0).

%C 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.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (20,-64).

%F a(n) = (4^(n-1) + 4^n - 1) * 3 * (4^(n-1))/2.

%F G.f.: -6*x*(x-1) / ((4*x-1)*(16*x-1)). - _Colin Barker_, Apr 30 2013

%e a(1) = 6 = 1 + 2 + 3.

%e 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 Cf. A007090, A010036, A026121, A026337, A101291.

%K easy,nonn,base

%O 1,1

%A _Jonathan Vos Post_, Sep 08 2006

%E More terms from _Colin Barker_, Apr 30 2013

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)