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A121544 Sum of all proper base 4 numbers with n digits (those not beginning with 0). 1
6, 114, 1896, 30624, 491136, 7862784, 125822976, 2013241344, 32212156416, 515395682304, 8246335635456, 131941389041664, 2111062300164096, 33776997104615424, 540431954881806336, 8646911282940739584, 138350580546379186176, 2213609288819376390144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (20,-64).

FORMULA

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

G.f.: -6*x*(x-1) / ((4*x-1)*(16*x-1)). - Colin Barker, Apr 30 2013

EXAMPLE

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

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.

CROSSREFS

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

Sequence in context: A194132 A194476 A059116 * A274786 A317172 A278752

Adjacent sequences:  A121541 A121542 A121543 * A121545 A121546 A121547

KEYWORD

easy,nonn,base

AUTHOR

Jonathan Vos Post, Sep 08 2006

EXTENSIONS

More terms from Colin Barker, Apr 30 2013

STATUS

approved

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Last modified September 18 12:39 EDT 2019. Contains 327170 sequences. (Running on oeis4.)