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A121515 Sum of all proper ternary numbers with n digits (those not beginning with 0). 0
3, 33, 315, 26163, 235953, 2125035, 19129689, 172180323, 1549662273, 13947078555, 125524061289, 1129717614483, 10167461718993, 91507165036875, 823564514029689, 7412080712360643, 66708726669526113, 600378540800575995, 5403406869529706889, 48630661832740930803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First differences of A026121. A026121 is partial sums of a(n). Sum of the first 2*(3^(n-1)) integers starting with 3^n. 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..20.

Index entries for linear recurrences with constant coefficients, signature (12,-27).

FORMULA

a(n) = (((3^n)*((3^n)-1)) - ((3^(n-1))*((3^(n-1)-1))))/2. a(n) = SUM[i=3^(n-1)..(3^n)-1]i.

a(n) = 3^n*(-1+4*3^n) for n>4. G.f.: -3*x*(23166*x^4-7758*x^3+x-1) / ((3*x-1)*(9*x-1)). - Colin Barker, Apr 30 2013

EXAMPLE

a(1) = 3 = 1 + 2.

a(2) = 33 = 10_3 + 11_3 + 12_3 + 20_3 + 21_3 + 22_3 = 3+4+5+6+7.

a(3) = 315 = 100_3 + 101_3 + 102_3 + 110_3 + 111_3 + 112_3 + 120_3 + 121_3 + 122_3 + 200_3 + 201_3 + 202_3 + 210_3 + 211_3 + 212_3 + 220_3 + 221_3 + 222_3 = 9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26.

CROSSREFS

Cf. A010036, A026121, A101291.

Sequence in context: A135697 A226508 A097486 * A221883 A002277 A001507

Adjacent sequences:  A121512 A121513 A121514 * A121516 A121517 A121518

KEYWORD

easy,nonn,base

AUTHOR

Jonathan Vos Post, Sep 07 2006

EXTENSIONS

More terms from Colin Barker, Apr 30 2013

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)