OFFSET
0,2
COMMENTS
Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301710. - Ray Chandler, Aug 30 2023
LINKS
Ray Chandler, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).
FORMULA
From Colin Barker, Apr 07 2018: (Start)
G.f.: (1 + 3*x + 3*x^2 + 3*x^3 + x^4) / ((1 - x)^3*(1 + x^2)).
a(n) = (1/8+i/8)*((3-3*i) + (-i)^(1+n) + i^n + (11-11*i)*n + (11-11*i)*n^2) where i=sqrt(-1).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>4. (End)
MATHEMATICA
LinearRecurrence[{3, -4, 4, -3, 1}, {1, 6, 17, 34, 56}, 100] (* Paolo Xausa, Jul 31 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 26 2018
EXTENSIONS
More terms from R. J. Mathar, Mar 31 2018
STATUS
approved