OFFSET

0,3

COMMENTS

Similar to A181388, this occurs as binary encoding of a straight n-omino lying on the y-axis, when the grid points of the first quadrant (N x N, N={0,1,2,...}) are given the weight 2^k, with k=0, 1,2, 3,4,5, ... filled in by antidiagonals.

Numbers k such that the k-th composition in standard order (row k of A066099) is a reversed initial interval. - Gus Wiseman, Apr 02 2020

EXAMPLE

Label the cells of an infinite square matrix with 0,1,2,3,... along antidiagonals:

0 1 3 6 10 ...

2 4 7 ...

5 8 ...

9 ...

....

Now any subset of these cells can be represented by the sum of 2 raised to the power written in the given cells. In particular, the subset consisting of the first cell in the first 1, 2, 3, ... rows is represented by 2^0, 2^0+2^2, 2^0+2^2+2^5, ...

MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;

normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];

Select[Range[0, 1000], normQ[stc[#]]&&Greater@@stc[#]&] (* Gus Wiseman, Apr 02 2020 *)

PROG

(PARI) t=0; vector(20, n, t+=2^(n*(n+1)/2-1)) \\ yields the vector starting with a[1]=1

(PARI) t=0; vector(20, n, if(n>1, t+=2^(n*(n-1)/2-1))) \\ yields the vector starting with 0

(Python)

a = 0

for n in range(1, 17): print(a, end =', '); a += 1<<(n-1)*(n+2)//2 # Ya-Ping Lu, Jan 23 2024

CROSSREFS

KEYWORD

nonn

AUTHOR

M. F. Hasler, Aug 28 2014

STATUS

approved