A372242 - OEIS

%I #65 May 20 2024 10:29:03

%S 1,9,11,19,31,49,81,129,211,339,551,889,1441,2329,3771,6099,9871,

%T 15969,25841,41809,67651,109459,177111,286569,463681,750249,1213931,

%U 1964179,3178111,5142289,8320401,13462689,21783091,35245779,57028871,92274649,149303521,241578169

%N a(n) = 10*Fibonacci(n) + (-1)^n.

%H Paolo Xausa, <a href="/A372242/b372242.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1).

%F Floor(a(n+2)/10) = A052952(n).

%F a(n) = 1 + A153382(n).

%F a(n) = 2*A371843(n) - (-1)^n.

%F a(n) = A022093(n) + (-1)^n.

%F G.f.: -(9*x^2+9*x+1)/((x+1)*(x^2+x-1)).

%F a(0) = 1. a(n) = -a(n-1) + 10*A000045(n+1) for n >= 1.

%F a(n) = a(n-4) + (2*A280154(n-2) = 5*A022112(n-3) = 10*A000032(n-2)) for n >= 4.

%e a(0) = 10*0 + 1 =  1,

%e a(1) = 10*1 - 1 =  9,

%e a(2) = 10*1 + 1 = 11,

%e a(3) = 10*2 - 1 = 19.

%t LinearRecurrence[{0, 2, 1}, {1, 9, 11}, 50] (* _Paolo Xausa_, May 20 2024 *)

%Y Cf. A000045, A022093, A153382, A052952, A371843.

%Y Cf. A000032, A022112, A280154.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Apr 23 2024