A129532 3n(n-1)4^(n-2).

0, 0, 6, 72, 576, 3840, 23040, 129024, 688128, 3538944, 17694720, 86507520, 415236096, 1962934272, 9160359936, 42278584320, 193273528320, 876173328384, 3942779977728, 17626545782784, 78340203479040, 346346162749440

Offset

0,3

Comments

Number of inversions in all 4-ary words of length n on {0,1,2,3}. Example: a(2)=6 because each of the words 10,20,30,21,31,32 has one inversion and the words 00,01,02,03,11,12,13,22,23,33 have no inversions. a(n)=Sum(k*A129531(n,k),k>=0). a(n)=6*A038845(n-2).

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Formula

G.f.=6x^2/(1-4x)^3.

Maple

seq(3*n*(n-1)*4^(n-2), n=0..25);

Mathematica

Table[3n(n-1)4^(n-2), {n, 0, 30}] (* or *) LinearRecurrence[{12, -48, 64}, {0, 0, 6}, 30] (* Harvey P. Dale, May 25 2018 *)

Crossrefs

Cf. A038845, A129531, A001788, A129530.

Sequence in context: A177468 A052791 A334327 * A151719 A118313 A283095

Adjacent sequences: A129529 A129530 A129531 * A129533 A129534 A129535

Keyword

nonn

Author

Emeric Deutsch, Apr 22 2007

Status

approved