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 A181630 Duplicate of A112310. 3

%I #10 Jun 04 2021 23:22:32

%S 1,1,2,2,2,3,2,3,3,3,4,3,3,4,3,4,4,4,5

%N Duplicate of A112310.

%C A181631 = number of leading 1's in Fibonacci Maximal notation.

%C This notation uses headings: (...5, 3, 2, 1); and fills in entries starting from the right, as opposed to the left. For example n=8 = 1011 = (5 + 2 + 1) as opposed to Minimal notation which would be (1100) = (5 + 3).

%C Conjectured row sums = A023610: (1, 3, 7, 15, 30, 58, ...).

%C Is this the same as A112310? - _R. J. Mathar_, Nov 03 2010

%C Contribution from _Gary W. Adamson_, Nov 03 2010: (Start)

%C The next row of 13 terms = (3, 4, 4, 5, 6, 4, 4, 5, 4, 5, 5, 5, 6), sum = 58. (End)

%F Count numbers of 1's in Fibonacci Maximal notation for n.

%e First few terms of the triangle:

%e 1;

%e 1, 2;

%e 2, 2, 3;

%e 2, 3, 3, 3, 4;

%e 3, 3, 4, 3, 4, 4, 4, 5;

%e ...

%e Example: 10 in Fibonacci Maximal = 1110, having three 1's, so a(10) = 3.

%Y Cf. A023610, A181631.