OFFSET
0,2
COMMENTS
Binomial transform of [1, 4, 8, 4, 2, -4, 8, -16, 32, -64, 128, ...]. - Gary W. Adamson, Feb 07 2010
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).
FORMULA
G.f.: -(x^4 + 2*x^3 + 4*x^2 + 2*x + 1)/((x-1)^2*(x^2-1)*(1-x)).
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5). - Wesley Ivan Hurt, Jan 20 2024
MAPLE
gf:= -(x^4+2*x^3+4*x^2+2*x+1)/((x-1)^2*(x^2-1)*(1-x)):
seq(coeff(series(gf, x, n+1), x, n), n=0..50);
MATHEMATICA
b[0]=1; b[1]=4; b[2]=8; b[3]=4; b[n_] := (-1)^n*2^(n-3); a[n_] := Sum[Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Aug 08 2012, after Gary W. Adamson *)
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 5, 17, 41, 83}, 80] (* Harvey P. Dale, Jan 22 2024 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
STATUS
approved