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A165410 Hankel transform of the transform of 2^n given by A165409. 1
1, 0, -4, -16, 0, 1024, 16384, 0, -16777216, -1073741824, 0, 17592186044416, 4503599627370496, 0, -1180591620717411303424, -1208925819614629174706176, 0, 5070602400912917605986812821504, 20769187434139310514121985316880384 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
CROSSREFS
Cf. A165409.
Sequence in context: A069019 A188249 A228559 * A016486 A065659 A305833
KEYWORD
sign
AUTHOR
Paul Barry, Sep 17 2009
STATUS
approved

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)