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Characteristic sequence for sequence A026905.
4

%I #14 Sep 25 2024 14:52:46

%S 1,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0

%N Characteristic sequence for sequence A026905.

%C This partition array is the member k=1 in the family M_0(k), with M_0(2)=M_0= A048996, M_0(3)= A134283, etc.

%C When read as partition array (tabf with sequence of row lengths given by the partition numbers A000041) in Abramowitz-Stegun order (see A117506 for the reference) a(n,k) is the characteristic partition array for the partition (1^n) of n.

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n)=1 if n from A026905, else 0.

%t terms = 105; nmax = 10;

%t pp = PartitionsP[Range[nmax]] // Accumulate;

%t a[n_] := If[n > pp[[-1]], Print["nmax = ", nmax, " too small"], Boole[ MemberQ[ pp, n]]];

%t Array[a, terms] (* _Jean-François Alcover_, Jun 19 2019 *)

%K nonn,easy,tabf

%O 1,1

%A _Wolfdieter Lang_, Nov 13 2007