OFFSET
0,3
COMMENTS
Binomial transform of A052964.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Amya Luo, Pattern Avoidance in Nonnesting Permutations, Undergraduate Thesis, Dartmouth College (2024). See p. 16.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).
FORMULA
G.f.: (1-3*x+2*x^2)/((1-3*x)*(1-x-x^2)).
a(n) = ((1+sqrt(5))/2)^n*(3/10-sqrt(5)/10) + ((1-sqrt(5))/2)^n*(3/10+sqrt(5)/10) + 3^n*2/5.
a(n) = Sum_{k=0..n} (-2*0^k-Fib(k-4)) * 3^(n-k).
MATHEMATICA
LinearRecurrence[{4, -2, -3}, {1, 1, 4}, 30] (* Paolo Xausa, Jun 20 2024 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 01 2004
STATUS
approved