OFFSET
0,1
COMMENTS
Generating floretion: - 1.5'i + 'j + 'k - .5i' + j' + k' + .5'ii' - .5'jj' - .5'kk' - 'ij' + 'ik' - 'ji' + .5'jk' + 2'ki' - .5'kj' + .5e
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).
FORMULA
G.f.: (3 -4*x -3*x^2)/((1-x)*(1+x)*(1-2*x-x^2)).
From Colin Barker, May 26 2016: (Start)
a(n) = 1 + (-1)^n + ((1+sqrt(2))^(1+n) - (1-sqrt(2))^(1+n))/(2*sqrt(2)).
a(n) = 2*a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) for n>3. (End)
a(n) = A000129(n+1) + 1 + (-1)^n. - G. C. Greubel, May 24 2021
MATHEMATICA
Table[Fibonacci[n+1, 2] +1+(-1)^n, {n, 0, 30}] (* G. C. Greubel, May 24 2021 *)
PROG
(PARI) Vec((3-4*x-3*x^2)/((1-x^2)*(1-2*x-x^2)) + O(x^50)) \\ Colin Barker, May 26 2016
(Magma) I:=[3, 2, 7, 12]; [n le 4 select I[n] else 2*Self(n-1) +2*Self(n-2) -2*Self(n-3) -Self(n-4): n in [1..31]]; // G. C. Greubel, May 24 2021
(Sage) [lucas_number1(n+1, 2, -1) +(1+(-1)^n) for n in (0..30)] # G. C. Greubel, May 24 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Feb 18 2006
STATUS
approved