cp's OEIS Frontend

A294199 Number of partitions of n into powers of 2 such that 1 and 2 cannot both be parts of a particular partition, and 4 and 8 cannot both be parts of a particular partition, and 16 and 32, and so on.

%I A294199 #17 Oct 25 2017 11:52:22
%S A294199 1,1,2,1,3,2,4,2,6,4,8,4,9,5,10,5,13,8,16,8,18,10,20,10,24,14,28,14,
%T A294199 30,16,32,16,38,22,44,22,48,26,52,26,60,34,68,34,72,38,76,38,85,47,94,
%U A294199 47,99,52,104,52,114,62,124,62,129,67,134,67,147,80,160
%N A294199 Number of partitions of n into powers of 2 such that 1 and 2 cannot both be parts of a particular partition, and 4 and 8 cannot both be parts of a particular partition, and 16 and 32, and so on.
%H A294199 Vaclav Kotesovec, <a href="/A294199/b294199.txt">Table of n, a(n) for n = 0..10000</a>
%H A294199 Bin Lan and James A. Sellers, <a href="https://www.emis.de/journals/INTEGERS/papers/p23/p23.Abstract.html">Properties of a Restricted Binary Partition Function a la Andrews and Lewis</a>, #A23 INTEGERS 15 (2015), p.2.
%F A294199 G.f.: Product_{k>=1} (1 - x^(2^(2*k-2) + 2^(2*k-1))) / ((1 - x^(2^(2*k-2))) * (1 - x^(2^(2*k-1)))).
%F A294199 G.f.: Product_{k>=1} (1 - x^(3*2^(2*k-2))) / (1 - x^(2^(k-1))).
%F A294199 For n>=1 a(2*n) = a(2*n-2) + a([n/2]).
%F A294199 For n>=1 a(2*n+1) = a(2*n) - a(2*n-1).
%e A294199 a(10) = 8 where the partitions are the following: 8+2, 8+1+1, 4+4+2, 4+2+2+2, 4+4+1+1, 4+1+1+1+1+1+1, 2+2+2+2+2, 1+1+1+1+1+1+1+1+1+1.
%t A294199 nmax = 20; CoefficientList[Series[Product[(1-x^(3*2^(2*k-2)))/(1-x^(2^(k-1))), {k, 1, nmax}], {x, 0, nmax}], x]
%t A294199 a[0] = 1; a[1] = 1; a[2] = 2; a[3] = 1; Flatten[{1, 1, 2, 1, Table[If[EvenQ[n], a[n] = a[n-2] + a[Floor[n/4]], a[n] = a[n-1] - a[n-2]], {n, 4, 100}]}]
%Y A294199 Cf. A070047.
%K A294199 nonn
%O A294199 0,3
%A A294199 _Vaclav Kotesovec_, Oct 24 2017