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An inventory sequence: the first row contains the value 1, subsequent rows contains the number of terms in prior rows whose binary expansions contain 2^0 (provided this number is nonzero), then the number of terms for 2^1 (provided it is > 0), then for 2^2, etc.
1

%I #7 Nov 21 2023 08:34:11

%S 1,1,2,2,1,3,2,4,4,4,4,2,4,5,4,5,5,7,8,6,10,8,8,11,2,9,10,11,5,12,12,

%T 12,8,12,12,15,12,13,13,19,16,16,14,21,18,2,17,17,23,19,5,22,19,25,19,

%U 9,26,22,26,21,13,28,25,29,24,17,31,25,31,28,22,34,28,35,32,27

%N An inventory sequence: the first row contains the value 1, subsequent rows contains the number of terms in prior rows whose binary expansions contain 2^0 (provided this number is nonzero), then the number of terms for 2^1 (provided it is > 0), then for 2^2, etc.

%H Rémy Sigrist, <a href="/A367292/a367292.png">Colored scatterplot of the first 2^20 terms</a> (where the color depends on the power of two appearing in the terms to be counted)

%H Rémy Sigrist, <a href="/A367292/a367292.gp.txt">PARI program</a>

%H <a href="/index/In#inventory">Index entries for sequences related to the inventory sequence</a>

%e As an irregular triangle this begins:

%e 1;

%e 1;

%e 2;

%e 2, 1;

%e 3, 2;

%e 4, 4;

%e 4, 4, 2;

%e 4, 5, 4;

%e 5, 5, 7;

%e 8, 6, 10;

%e 8, 8, 11, 2;

%e 9, 10, 11, 5;

%e 12, 12, 12, 8;

%e 12, 12, 15, 12;

%e 13, 13, 19, 16;

%e 16, 14, 21, 18, 2;

%e ...

%o (PARI) See Links section.

%Y Cf. A342585.

%K nonn,base,tabf

%O 1,3

%A _Rémy Sigrist_, Nov 12 2023