

A246534


Sum_{k=1,n} 2^(T(k)1), where T(k)=k(k+1)/2 are the triangular numbers A000217; for n=0 the empty sum a(0)=0.


17



0, 1, 5, 37, 549, 16933, 1065509, 135283237, 34495021605, 17626681066021, 18032025190548005, 36911520172609651237, 151152638972001256489509, 1238091191924352276155613733, 20283647694843594776223406899749, 664634281540152780046679753547072037
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OFFSET

0,3


COMMENTS

Similar to A181388, this occurs as binary encoding of a straight nomino lying on the yaxis, 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 kth composition in standard order (row k of A066099) is a reversed initial interval.  Gus Wiseman, Apr 02 2020


LINKS

Table of n, a(n) for n=0..15.


EXAMPLE

Label the cells of an infinite square matrix with 0,1,2,3... following 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)/21)) \\ yields the vector starting with a[1]=1
(PARI) t=0; vector(20, n, if(n>1, t+=2^(n*(n1)/21))) \\ yields the vector starting with 0


CROSSREFS

The version for prime (rather than binary) indices is A002110.
The nonstrict generalization is A114994.
The nonreversed version is A164894.
Intersection of A333256 and A333217.
Cf. A000120, A029931, A048793, A066099, A070939, A124766, A228351, A233564, A272919, A333218.
Sequence in context: A286928 A321042 A244820 * A095957 A121834 A215233
Adjacent sequences: A246531 A246532 A246533 * A246535 A246536 A246537


KEYWORD

nonn


AUTHOR

M. F. Hasler, Aug 28 2014


STATUS

approved



