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A114116 1's-counting matrix: row sums give number of 1's in binary expansion of n+1. 2

%I #2 Mar 30 2012 18:59:13

%S 1,0,1,2,-1,1,-1,2,-1,1,1,0,1,-1,1,1,0,0,1,-1,1,3,-2,2,-1,1,-1,1,-2,3,

%T -2,2,-1,1,-1,1,0,1,0,0,1,-1,1,-1,1,0,1,0,0,0,1,-1,1,-1,1,2,-1,2,-2,2,

%U -1,1,-1,1,-1,1,0,1,-1,2,-2,2,-1,1,-1,1,-1,1,2,-1,1,0,0,0,1,-1,1,-1,1,-1,1,2,-1,1,0,0,0,0,1,-1,1,-1,1,-1,1,4,-3,3,-2,2

%N 1's-counting matrix: row sums give number of 1's in binary expansion of n+1.

%C First column is -A037861(n+1). Row sums are A000120. Product of partial sum matrix (1/(1-x),x) and A114115. Inverse is A114117.

%e Triangle begins

%e 1;

%e 0, 1;

%e 2,-1, 1;

%e -1, 2,-1, 1;

%e 1, 0, 1,-1, 1;

%e 1, 0, 0, 1,-1, 1;

%e 3,-2, 2,-1, 1,-1, 1;

%K sign,tabl

%O 0,4

%A _Paul Barry_, Nov 13 2005

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Last modified April 16 04:17 EDT 2024. Contains 371696 sequences. (Running on oeis4.)