OFFSET
0,3
COMMENTS
Powers of two occurring in this sequence are based on the hexagonal spiral pattern of A049450 and A049451 (see A152749):
.
16--15--14
/ \
17 5---4 13
/ / \ \
18 6 0 3 12
/ / / / /
19 7 1---2 11 26
\ \ / /
20 8---9--10 25
\ /
21--22--23--24
.
The powers, (0,-oo,2,4,-oo,10,14,-oo,24,30,-oo,...) correspond to vertically joining pairs on the (0,4) and (0,2) radial lines, with -oo corresponding to the jump to the next pair.
The Hankel transforms of transforms of r^n behave similarly -- we get 1, 0, -r^2, -r^4, 0, r^10, r^14, ....
Note the Somos-4 property: a(3n) = 4*a(3n-1)*a(3n-3)/e(3n-4). Related to elliptic curve y^2 = 1 - 8x^3 in g.f. of A165409.
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Barry, Sep 17 2009
STATUS
approved