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

%I A225178 #15 Feb 28 2024 06:19:55
%S A225178 1,2,6,16,48,140,408,1224,3640,10824,32192,96576,288912,864288,
%T A225178 2585584,7735104,23205312,69551552,208461504,624806688,1872691488,
%U A225178 5612903296,16838709888,50500659456,151455567744,454227600128,1362265877376
%N A225178 The generalized Conway-Guy sequence d_2(n).
%H A225178 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 A225178 Bae and Choi define this sequence via a collection of recurrences.
%p A225178 b := proc(n)
%p A225178     round(sqrt(2*n-2)) ;
%p A225178 end proc:
%p A225178 d := proc(k,n)
%p A225178     option remember;
%p A225178     if n = 1 then
%p A225178         1;
%p A225178     else
%p A225178         add( k*procname(k,i),i=n-b(n)..n-1 ) ;
%p A225178     end if;
%p A225178 end proc:
%p A225178 A225178 := proc(n)
%p A225178     d(2,n) ;
%p A225178 end proc: # _R. J. Mathar_, Jul 09 2013
%t A225178 b[n_] := Round[Sqrt[2n-2]];
%t A225178 d[k_, n_] := d[k, n] = If[n == 1, 1, Sum[k*d[k, i], {i, n-b[n], n-1}]];
%t A225178 a[n_] := d[2, n];
%t A225178 Table[a[n], {n, 1, 27}] (* _Jean-François Alcover_, Feb 27 2024, after _R. J. Mathar_ *)
%Y A225178 Cf. A005318, A005230, A002024.
%K A225178 nonn
%O A225178 1,2
%A A225178 _N. J. A. Sloane_, May 02 2013