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Number of partitions of n into sums of exactly two distinct powers of 2.
5

%I #12 Aug 01 2023 06:56:07

%S 0,0,1,0,1,2,0,1,3,2,2,5,2,3,8,4,6,12,6,11,16,11,16,24,17,23,34,26,35,

%T 50,35,50,67,55,72,93,76,99,126,112,135,171,150,186,229,210,249,304,

%U 280,336,398,380,443,526,499,584,680,665,759,886,858,985,1136,1123

%N Number of partitions of n into sums of exactly two distinct powers of 2.

%H David A. Corneth, <a href="/A091889/b091889.txt">Table of n, a(n) for n = 1..10000</a>

%e a(9)=3: 9 = (2^3+2^0) = (2^2+2^1)+(2^1+2^0) = (2^1+2^0)+(2^1+2^0)+(2^1+2^0).

%t With[{max = 64}, m = Select[Range[max], DigitCount[#, 2, 1] == 2 &]; a[n_] := Length@ IntegerPartitions[n, n, m]; Array[a, max]] (* _Amiram Eldar_, Aug 01 2023 *)

%Y Cf. A018819, A018900, A091890, A000120, A000041, A091893, A091891.

%K nonn

%O 1,6

%A _Reinhard Zumkeller_, Feb 10 2004