|
%I #18 Mar 07 2024 17:27:32
%S -3,1,-9,25,-33,49,-129,289,-513,961,-2049,4225,-8193,16129,-32769,
%T 66049,-131073,261121,-524289,1050625,-2097153,4190209,-8388609,
%U 16785409,-33554433,67092481,-134217729,268468225,-536870913,1073676289,-2147483649
%N a(2*n) = -(2^(2*n+1) + 1), a(2*n+1) = (2^(n+1) - (-1)^n)^2.
%C This sequence appears to have the property that for m > n: if s divides a(n) and a(m) then s also divides a(2m-n). For example, 11 divides -33 = a(4), 11 divides -32769 = a(14) and 11 divides a(2*14-4) = a(24) = -33554433.
%C Floretion Algebra Multiplication Program, FAMP Code: 4tesseq[ - .75'i - .75i' - .75'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .75e]
%H G. C. Greubel, <a href="/A105951/b105951.txt">Table of n, a(n) for n = 0..1000</a>
%H Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-floretion.html">Sequences Related to Floretions</a>
%F G.f.: -(3 +8*x +18*x^2 +16*x^3)/((2*x+1)*(x+1)*(2*x^2+1)).
%t 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 *)
%o (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
%o (Python)
%o def A105951(n): return (1<<n+1)+1+(1<<m+2 if (m:=n>>1)&1 else -(1<<m+2)) if n&1 else -(1<<n+1)-1 # _Chai Wah Wu_, Mar 07 2024
%K easy,sign
%O 0,1
%A _Creighton Dement_, Apr 27 2005
|
