A329114 - OEIS

%I #5 Nov 23 2019 13:41:08

%S 0,0,1,3,7,21,43,129,259,777,1555,4665,9331,27993,55987,167961,335923,

%T 1007769,2015539,6046617,12093235,36279705,72559411,217678233,

%U 435356467,1306069401,2612138803,7836416409,15672832819,47018498457,94036996915,282110990745

%N a(n) = floor(A026532(n)/5).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,7,0,-6).

%F a(n+1) = 3*a(n) if n is odd, a(n+1) = 2*a(n)+1 if n is even.

%F a(n) = f(3^f(n/2) * 2^f((n-1)/2) / 5), where f = floor.

%F G.f.: (x^2 (1 + 3 x))/((-1 + x) (1 + x) (-1 + 6 x^2)).

%F a(n) = 7*a(n-2) - 6*a(n-4).

%t s[1] = 1; s[n_] := If[IntegerQ[n/2], 3*s[n - 1], 2*s[n - 1]]

%t Table[s[n], {n, 1, 20}] (* A026549 *)

%t Table[Floor[s[n]/5], {n, 1, 50}] (* A329114 *)

%Y Cf. A026532, A329115.

%K nonn,easy

%O 1,4

%A _Clark Kimberling_, Nov 10 2019