A175357 - OEIS

%I #10 Feb 06 2019 16:35:55

%S 1,1,2,2,2,2,1,2,1,2,1,3,2,3,2,3,1,3,2,3,3,2,1,3,2,2,3,3,1,3,3,3,2,2,

%T 1,3,3,2,2,3,1,3,3,2,3,2,1,2,2,3,3,3,1,2,3,3,2,3,1,2,3,3,3,2,1,2,3,2,

%U 3,3,2,3,1,3,2,3,2,3,1,3,3,2,2,3,1,2,3

%N Irregular array: Row n contains the run-lengths (of runs of both 0's and 1's) of the binary representation of A175356(n).

%C This array orders the distinct permutations each of one 1, two 2's, three 3's..., m number of m's, for a positive integer m.

%C The number of terms per row is nondecreasing. There are exactly (m(m+1)/2)!/product{k=1 to m}k! rows in the sequence each of m(m+1)/2 terms, for all m >= 1, and none of any other number of terms.

%H Rémy Sigrist, <a href="/A175357/a175357.gp.txt">PARI program for A175357</a>

%e 8984, the fifth term of A175356, is 10001100011000 in binary. There is a run of one 1, followed by a run of three 0's, followed by a run of two 1's, followed by a run of three 0's, followed by a run of two 1's, followed finally by a run of three 0's. So, row 5 is 1,3,2,3,2,3.

%o (PARI) See Links section.

%Y Cf. A175356, A022915.

%K base,nonn,tabf

%O 1,3

%A _Leroy Quet_, Apr 22 2010

%E Example changed and tabf keyword added by _Leroy Quet_, Apr 27 2010

%E More terms from _Rémy Sigrist_, Feb 06 2019