A134286 Characteristic sequence for sequence A026905.

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, 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, 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

Offset: 1

Author

Wolfdieter Lang, Nov 13 2007

Keywords

• nonn
• easy
• tabf

Comments

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.

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.

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for characteristic functions

Programs

Mathematica

terms = 105; nmax = 10;
pp = PartitionsP[Range[nmax]] // Accumulate;
a[n_] := If[n > pp[[-1]], Print["nmax = ", nmax, " too small"], Boole[ MemberQ[ pp, n]]];
Array[a, terms] (* Jean-François Alcover, Jun 19 2019 *)

Formula

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