A054244 Number of partitions of n into distinct positive parts <= n, with parts combined by IOR (inclusive or).

1, 1, 5, 1, 5, 5, 109, 1, 5, 5, 109, 5, 109, 109, 32297, 1, 5, 5, 109, 5, 109, 109, 32297, 5, 109, 109, 32297, 109, 32297, 32297, 2147321017, 1, 5, 5, 109, 5, 109, 109, 32297, 5, 109, 109, 32297, 109, 32297, 32297, 2147321017, 5, 109, 109, 32297, 109, 32297

Offset

1,3

Links

T. D. Noe, Table of n, a(n) for n=1..1000

D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.

Formula

a(n) = A003465(A000120(n)).

Example

a(3)=5 thus: 3 3+2 3+1 3+2+1 2+1 (with "+" meaning IOR).

Mathematica

A003465[n_] := Sum[(-1)^k*Binomial[n, k]*2^(2^(n - k)), {k, 0, n}]/2; a[n_] := A003465[DigitCount[n, 2, 1]]; Table[a[n], {n, 1, 53}] (* Jean-François Alcover, Nov 21 2012, from formula *)

Crossrefs

Cf. A003465 (if duplicates are removed from the current sequence), A000120, A054243 (XOR version).

Cf. also A087079.

Sequence in context: A162797 A087232 A151780 * A093562 A081774 A103193

Adjacent sequences: A054241 A054242 A054243 * A054245 A054246 A054247

Keyword

easy,nonn,nice

Author

Marc LeBrun, Feb 08 2000

Status

approved