A382656 a(n) = L(2*n+1)+4*n+2.

3, 10, 21, 43, 94, 221, 547, 1394, 3605, 9387, 24518, 64125, 167811, 439258, 1149909, 3010411, 7881262, 20633309, 54018595, 141422402, 370248533, 969323115, 2537720726, 6643838973, 17393796099, 45537549226, 119218851477, 312119005099, 817138163710, 2139295485917

Offset

0,1

Comments

For n >= 1, a(n) is also the number of minimum total dominating sets in the Lindgren-Sousselier graph on 6*n+4 vertices.

Links

Table of n, a(n) for n=0..29.

Eric Weisstein's World of Mathematics, Lindgren-Sousselier Graphs.

Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.

Index entries for linear recurrences with constant coefficients, signature (5,-8,5,-1).

Formula

G.f.: (1+x)*(3-8*x+3*x^2)/((-1+x)^2*(1-3*x+x^2)).

a(n) = 5*a(n-1)-8*a(n-2)+5*a(n-3)-a(n-4).

a(n) = A002878(n) + A016825(n).

Mathematica

Table[LucasL[2 n + 1] + 4 n + 2, {n, 0, 20}]
LinearRecurrence[{5, -8, 5, -1}, {10, 21, 43, 94}, {0, 20}]
CoefficientList[Series[((1 + x) (3 - 8 x + 3 x^2))/((-1 + x)^2 (1 - 3 x + x^2)), {x, 0, 20}], x]

Crossrefs

Cf. A000032, A000204, A002878, A016825.

Sequence in context: A210980 A207380 A268348 * A117495 A007687 A330273

Adjacent sequences: A382653 A382654 A382655 * A382657 A382658 A382659

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 02 2025

Status

approved