OFFSET
0,3
COMMENTS
The three sequences of the definition share the same special recurrence which reflects that each equals its own sequence of third differences.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1,2,2).
FORMULA
a(n+8) == a(n) (mod 10), n > 1.
a(2*n+1) - a(2*n) = 1.
a(2*n) = A000975(n+1), n>0 (bisection).
From R. J. Mathar, Nov 22 2009: (Start)
a(n) = -a(n-1) +a(n-2) +a(n-3) +2*a(n-4) +2*a(n-5), n>6.
G.f.: x*(3*x+4*x^2+5*x^3+4*x^4+2*x^5+1)/((1+x)*(1-2*x^2)*(1+x^2)). (End)
MATHEMATICA
CoefficientList[Series[x*(3*x + 4*x^2 + 5*x^3 + 4*x^4 + 2*x^5 + 1)/((1 + x)*(1 - 2*x^2)*(1 + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Oct 03 2017 *)
LinearRecurrence[{-1, 1, 1, 2, 2}, {0, 1, 2, 3, 5, 6, 10}, 50] (* Harvey P. Dale, Feb 18 2023 *)
PROG
(PARI) x='x+O('x^50); concat(0, Vec(x*(3*x+4*x^2+5*x^3+4*x^4 +2*x^5+ 1)/((1+x)*(1-2*x^2)*(1+x^2)))) \\ G. C. Greubel, Oct 03 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, May 13 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Nov 22 2009
STATUS
approved