OFFSET
0,5
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,1,2).
FORMULA
a(n+1) = 2*a(n) - A104581(n+6).
a(n) + a(n+1) = A113405(n).
a(n) + a(n+3) = A001045(n).
a(n+2) = a(n) + A131666(n).
From Thomas Scheuerle, Oct 18 2021: (Start)
G.f.: (x^4-x^3+2x-1)/((2*x^3-3*x^2+3*x-1)*(x+1)^2).
A172481(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*a(2*n-k). With negative sign for ...*a(1+2*n-k) and ...*a(3+2*n-k) too.
A175656(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*a(2+2*n-k).
A136298(n+1) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*a(4+2*n-k).
A348407(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*(a(2+2*n-k) - 2*a(1+2*n-k) - a(2*n-k)).
(End)
MATHEMATICA
CoefficientList[ Series[(x^4-x^3+2x-1)/((2*x^3-3*x^2+3*x-1)*(x+1)^2), {x, 0, 40}], x] (* Thomas Scheuerle, Oct 17 2021 *)
nxt[{n_, a_}]:={n+1, Round[(2^n)/9]-a}; NestList[nxt, {0, 1}, 40][[All, 2]] (* or *) LinearRecurrence[{1, 2, -1, 1, 2}, {1, -1, 1, -1, 2}, 40] (* Harvey P. Dale, Apr 28 2022 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, Oct 17 2021
EXTENSIONS
a(22)-a(36) from Thomas Scheuerle, Oct 17 2021
STATUS
approved