A344109 - OEIS

%I #29 May 24 2021 05:45:56

%S 4,1,9,11,29,51,109,211,429,851,1709,3411,6829,13651,27309,54611,

%T 109229,218451,436909,873811,1747629,3495251,6990509,13981011,

%U 27962029,55924051,111848109,223696211,447392429,894784851,1789569709,3579139411,7158278829,14316557651,28633115309,57266230611,114532461229,229064922451

%N a(n) = (5*2^n + 7*(-1)^n)/3.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n+1) = 5*2^n - a(n) for n >= 0, with a(0) = 4.

%F a(n+2) = 5*2^n + a(n) for n >= 0, with a(0) = 4, a(1) = 1.

%F a(n+3) = 15*2^n - a(n) for n >= 0, with a(0) = 4, a(1) = 1, a(2) = 9.

%F a(n) = A001045(n+2) + A154879(n).

%F a(2*n+1) = A321421(n).

%F a(n) = a(n-1) + 2*a(n-2) for n >= 2. - _Pontus von Brömssen_, May 09 2021

%F G.f.: (4 - 3*x)/(1 - x - 2*x^2). - _Stefano Spezia_, May 10 2021

%F a(n) = 2*A014551(n) - A001045(n).

%F a(n) = abs(A156550(n)) - (-1)^n.

%F a(n+3) = a(n) + 7*A084214(n+1) for n >= 0, with a(0) = 4.

%F a(n) = 5*A001045(n+1) - A084214(n+1) for n >= 0.

%F a(n) = A084214(n+1) + 3*(-1)^n for n >= 0.

%t LinearRecurrence[{1,2}, {4,1}, 28] (* _Amiram Eldar_, May 10 2021 *)

%Y Cf. A001045, A020714, A110286, A154879, A321421.

%Y Cf. A014551, A156550, A084214.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, May 09 2021