

A105951


a(2*n) = (2^(2*n+1) + 1), a(2*n+1) = (2^(n+1)  (1)^n)^2.


2



3, 1, 9, 25, 33, 49, 129, 289, 513, 961, 2049, 4225, 8193, 16129, 32769, 66049, 131073, 261121, 524289, 1050625, 2097153, 4190209, 8388609, 16785409, 33554433, 67092481, 134217729, 268468225, 536870913, 1073676289, 2147483649
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OFFSET

0,1


COMMENTS

This sequence appears to have the property that for m > n: if s divides a(n) and a(m) then s also divides a(2mn). For example, 11 divides 33 = a(4), 11 divides 32769 = a(14) and 11 divides a(2*144) = a(24) = 33554433.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Robert Munafo, Sequences Related to Floretions


FORMULA

G.f.: (3 +8*x +18*x^2 +16*x^3)/((2*x+1)*(x+1)*(2*x^2+1)).


MATHEMATICA

CoefficientList[Series[(3 + 8*x + 18*x^2 + 16*x^3)/((2*x + 1)*(x + 1)*(2*x^2 + 1)), {x, 0, 50}], x] (* G. C. Greubel, Jan 01 2018 *)


PROG

Floretion Algebra Multiplication Program, FAMP Code: 4tesseq[  .75'i  .75i'  .75'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj'  .75e]
(PARI) x='x+O('x^30); Vec((3 + 8*x + 18*x^2 + 16*x^3)/((2*x + 1)*(x + 1)*(2*x^2 + 1))) \\ G. C. Greubel, Jan 01 2018


CROSSREFS

Sequence in context: A157403 A225118 A273464 * A038202 A128415 A227795
Adjacent sequences: A105948 A105949 A105950 * A105952 A105953 A105954


KEYWORD

easy,sign


AUTHOR

Creighton Dement, Apr 27 2005


STATUS

approved



