A099164 a(n) = (L(n+2) + 2*3^n)/5.

1, 2, 5, 13, 36, 103, 301, 890, 2649, 7913, 23684, 70963, 212745, 638002, 1913629, 5740277, 17219844, 51657935, 154971221, 464909482, 1394721681, 4184154097, 12552444580, 37657305083, 112971868881, 338915531618, 1016746473461, 3050239223965, 9150717354084

Offset

0,2

Comments

Binomial transform of A099163.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).

Formula

G.f.: (1-2x-x^2)/((1-3x)(1-x-x^2)); a(n)=4a(n-1)-2a(n-2)-3a(n-3); a(n)=((1+sqrt(5))/2)^n(3/10+sqrt(5)/10)+((1-sqrt(5))/2)^n(3/10-sqrt(5)/10)+2*3^n/5; a(n)=sum{k=0..n, 3^k(0^(n-k)-Fib(n-k))}.

Maple

a:= n-> (<<1|2|0>, <1|1|1>, <0|1|2>>^n)[3, 3]:
seq(a(n), n=0..28);  # Alois P. Heinz, Apr 17 2026

Mathematica

LinearRecurrence[{4, -2, -3}, {1, 2, 5}, 30] (* Harvey P. Dale, Dec 08 2022 *)

Crossrefs

Cf. A000032, A000045.

Sequence in context: A223096 A277996 A370168 * A358460 A289453 A339290

Adjacent sequences: A099161 A099162 A099163 * A099165 A099166 A099167

Keyword

easy,nonn

Author

Paul Barry, Oct 01 2004

Status

approved