A105951 a(2*n) = -(2^(2*n+1) + 1), a(2*n+1) = (2^(n+1) - (-1)^n)^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

Offset: 0

Author

Creighton Dement, Apr 27 2005

Keywords

• easy
• sign

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(2m-n). For example, 11 divides -33 = a(4), 11 divides -32769 = a(14) and 11 divides a(2*14-4) = a(24) = -33554433.

Floretion Algebra Multiplication Program, FAMP Code: 4tesseq[ - .75'i - .75i' - .75'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .75e]

Links

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

Programs

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 *)

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

Python

def A105951(n): return (1<>1)&1 else -(1<Chai Wah Wu, Mar 07 2024

Formula

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