A169637 - OEIS

%I #14 Jun 29 2021 17:18:53

%S 1,1,1,4,20,60,420,3360,15120,151200,831600,3326400,43243200,

%T 302702400,1513512000,24216192000,411675264000,3705077376000,

%U 70396470144000,703964701440000,14783258730240000,162615846032640000,1246721486250240000,7480328917501440000

%N The number of permutations of the first n elements of the Hofstaedter Q-sequence (A005185), augmented by Q(0)=1.

%C An augmented Hofstadter sequence 1,1,1,2,3,3,... is defined by adding a single 1 in front of A005185. a(n) is the number of permutations using the first n+1 elements, 1 up to A005185(n), of this augmented sequence.

%H Rémy Sigrist, <a href="/A169637/a169637.gp.txt">PARI program for A169637</a>

%e For n=3, the first 4 elements of the augmented sequence are (1,1,1,2), with a(3)=4 permutations, namely (1,1,1,2), (1,1,2,1), (1,2,1,1) and (2,1,1,1).

%t f[0] = 1; f[1] = 1; f[2] = 1;

%t f[n_] := f[n] = f[n - f[n - 1]] + f[n - f[n - 2]];

%t a[m_] := Length[Permutations[Table[f[i], {i, 0, m}]]];

%t (* b = Table[a[m], {m, 0, 10}]  *)

%t (* A much better way to compute the terms is to use the multinomials of the multiplicities of the terms of A005229! - _Joerg Arndt_, Dec 23 2014 *)

%o (PARI) See Links section.

%Y Cf. A005185.

%K nonn

%O 0,4

%A _Roger L. Bagula_, Apr 04 2010

%E Definition clarified, comment and example added - _R. J. Mathar_, Dec 08 2010

%E More terms from _Rémy Sigrist_, Jun 29 2021