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A225178 The generalized Conway-Guy sequence d_2(n). 1

%I #15 Feb 28 2024 06:19:55

%S 1,2,6,16,48,140,408,1224,3640,10824,32192,96576,288912,864288,

%T 2585584,7735104,23205312,69551552,208461504,624806688,1872691488,

%U 5612903296,16838709888,50500659456,151455567744,454227600128,1362265877376

%N The generalized Conway-Guy sequence d_2(n).

%H Jaegug Bae and Sungjin Choi, <a href="https://doi.org/10.4134/JKMS.2003.40.5.757">A generalization of a subset-sum-distinct sequence</a>, J. Korean Math. Soc. 40 (2003), no. 5, 757--768. MR1996839 (2004d:05198). See b(n).

%F Bae and Choi define this sequence via a collection of recurrences.

%p b := proc(n)

%p round(sqrt(2*n-2)) ;

%p end proc:

%p d := proc(k,n)

%p option remember;

%p if n = 1 then

%p 1;

%p else

%p add( k*procname(k,i),i=n-b(n)..n-1 ) ;

%p end if;

%p end proc:

%p A225178 := proc(n)

%p d(2,n) ;

%p end proc: # _R. J. Mathar_, Jul 09 2013

%t b[n_] := Round[Sqrt[2n-2]];

%t d[k_, n_] := d[k, n] = If[n == 1, 1, Sum[k*d[k, i], {i, n-b[n], n-1}]];

%t a[n_] := d[2, n];

%t Table[a[n], {n, 1, 27}] (* _Jean-François Alcover_, Feb 27 2024, after _R. J. Mathar_ *)

%Y Cf. A005318, A005230, A002024.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 02 2013

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)