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

%I A054244 #23 Jan 20 2024 15:44:28
%S A054244 1,1,5,1,5,5,109,1,5,5,109,5,109,109,32297,1,5,5,109,5,109,109,32297,
%T A054244 5,109,109,32297,109,32297,32297,2147321017,1,5,5,109,5,109,109,32297,
%U A054244 5,109,109,32297,109,32297,32297,2147321017,5,109,109,32297,109,32297
%N A054244 Number of partitions of n into distinct positive parts <= n, with parts combined by IOR (inclusive or).
%H A054244 T. D. Noe, <a href="/A054244/b054244.txt">Table of n, a(n) for n=1..1000</a>
%H A054244 D. Applegate, M. LeBrun, N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Sloane/carry2.html">Dismal Arithmetic</a>, J. Int. Seq. 14 (2011) # 11.9.8.
%F A054244 a(n) = A003465(A000120(n)).
%e A054244 a(3)=5 thus: 3 3+2 3+1 3+2+1 2+1 (with "+" meaning IOR).
%t A054244 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 *)
%Y A054244 Cf. A003465 (if duplicates are removed from the current sequence), A000120, A054243 (XOR version).
%Y A054244 Cf. also A087079.
%K A054244 easy,nonn,nice
%O A054244 1,3
%A A054244 _Marc LeBrun_, Feb 08 2000