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

1, 2, 6, 16, 48, 140, 408, 1224, 3640, 10824, 32192, 96576, 288912, 864288, 2585584, 7735104, 23205312, 69551552, 208461504, 624806688, 1872691488, 5612903296, 16838709888, 50500659456, 151455567744, 454227600128, 1362265877376

Offset: 1

Author

N. J. A. Sloane, May 02 2013

Keywords

• nonn

Links

• Jaegug Bae and Sungjin Choi, A generalization of a subset-sum-distinct sequence, J. Korean Math. Soc. 40 (2003), no. 5, 757--768. MR1996839 (2004d:05198). See b(n).

Crossrefs

Cf. A005318, A005230, A002024.

Programs

Maple

b := proc(n)
    round(sqrt(2*n-2)) ;
end proc:
d := proc(k,n)
    option remember;
    if n = 1 then
        1;
    else
        add( k*procname(k,i),i=n-b(n)..n-1 ) ;
    end if;
end proc:
A225178 := proc(n)
    d(2,n) ;
end proc: # R. J. Mathar, Jul 09 2013

Mathematica

b[n_] := Round[Sqrt[2n-2]];
d[k_, n_] := d[k, n] = If[n == 1, 1, Sum[k*d[k, i], {i, n-b[n], n-1}]];
a[n_] := d[2, n];
Table[a[n], {n, 1, 27}] (* Jean-François Alcover, Feb 27 2024, after R. J. Mathar *)

Formula

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