OFFSET
0,2
LINKS
Tomislav Doslic and I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276. See Prop. 7.1.
Index entries for linear recurrences with constant coefficients, signature (0,3,2,-3,-4,0,2,1).
FORMULA
From Colin Barker, Apr 25 2017: (Start)
G.f.: (1 + 3*x - 4*x^3 - 3*x^4 + x^5 + 2*x^6 + x^7) / ((1 - x)*(1 + x)*(1 - x^2 - x^3)^2).
a(n) = 3*a(n-2) + 2*a(n-3) - 3*a(n-4) - 4*a(n-5) + 2*a(n-7) + a(n-8) for n>7. (End)
MAPLE
MATHEMATICA
(* b is A000931 *)
b[n_] := b[n] = Which[n == 0, 1, n <= 2, 0, True, b[n-2] + b[n-3]];
psi[n_] := b[n+6];
a[n_] := Sum[psi[k-1]*psi[n-k-1], {k, 0, n}] + (1-(-1)^n)/2;
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 19 2023, after Maple code *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 23 2017
STATUS
approved