login
A285184
a(n) = 2*a(n-1) + a(n-3) with initial terms 1,3,5.
1
1, 3, 5, 11, 25, 55, 121, 267, 589, 1299, 2865, 6319, 13937, 30739, 67797, 149531, 329801, 727399, 1604329, 3538459, 7804317, 17212963, 37964385, 83733087, 184679137, 407322659, 898378405, 1981435947, 4370194553, 9638767511, 21258970969, 46888136491, 103415040493, 228089051955
OFFSET
0,2
COMMENTS
The sequences in Prop. 5.1 and 5.2 should also be added to the OEIS.
LINKS
Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276. See Cor. 4.3.
FORMULA
G.f.: (1 + x - x^2) / (1 - 2*x - x^3). - Colin Barker, Apr 23 2017
MAPLE
a:=proc(n) option remember;
if n=0 then 1
elif n=1 then 3
elif n=2 then 5
else 2*a(n-1)+a(n-3); fi;
end;
[seq(a(n), n=0..40)];
MATHEMATICA
LinearRecurrence[{2, 0, 1}, {1, 3, 5}, 40] (* Harvey P. Dale, May 26 2023 *)
PROG
(PARI) Vec((1 + x - x^2) / (1 - 2*x - x^3) + O(x^40)) \\ Colin Barker, Apr 23 2017
CROSSREFS
Cf. A193641.
Sequence in context: A259643 A167796 A261896 * A018008 A104545 A027050
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 23 2017
STATUS
approved