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

Author

Marc LeBrun, Feb 08 2000

Keywords

• easy
• nonn
• nice

Examples

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

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.

Crossrefs

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

Cf. also A087079.

Programs

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 *)

Formula

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