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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 (list; graph; refs; listen; history; text; internal format)
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

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)/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

CROSSREFS

The version for prime (rather than binary) indices is A002110.

The non-strict generalization is A114994.

The non-reversed 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

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Last modified May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)