

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.


1



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 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.


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, ...


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

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



