A285184 a(n) = 2*a(n-1) + a(n-3) with initial terms 1,3,5.

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

Colin Barker, Table of n, a(n) for n = 0..1000

Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276. See Cor. 4.3.

Index entries for linear recurrences with constant coefficients, signature (2,0,1).

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

Adjacent sequences: A285181 A285182 A285183 * A285185 A285186 A285187

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 23 2017

Status

approved