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A069515 Number of transpositions (interchanges of adjacent digits, sometimes called inversions) needed to change all n-digit base 3 numbers into nondecreasing order. 0
0, 3, 24, 135, 648, 2835, 11664, 45927, 174960, 649539, 2361960, 8444007, 29760696, 103630995, 357128352, 1219657095, 4132485216, 13904090883, 46490458680, 154580775111, 511395045480, 1684116865683, 5523066491184 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The corresponding problem for base 2 numbers gives a(n)=A001793(n-1) for n=2,3,4,....

LINKS

Table of n, a(n) for n=1..23.

Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

FORMULA

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

a(n) = (n-1)(n+1)3^(n-2). - Ralf Stephan, Sep 02 2003

G.f.: 3*x^2*(1-x)/(1-3*x)^3. - Colin Barker, May 01 2012

EXAMPLE

The base 3 number 1210 requires 4 transpositions: 1210->1201->1021->0121->0112.

CROSSREFS

Cf. A064017.

Sequence in context: A305543 A183900 A001089 * A206949 A215636 A056350

Adjacent sequences:  A069512 A069513 A069514 * A069516 A069517 A069518

KEYWORD

nonn,base,easy

AUTHOR

John W. Layman, Apr 16 2002

EXTENSIONS

Corrected by T. D. Noe, Nov 01 2006

STATUS

approved

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Last modified August 12 16:40 EDT 2020. Contains 336439 sequences. (Running on oeis4.)