A164265 - OEIS

%I #16 Apr 18 2024 06:11:58

%S 4,7,19,28,64,91,199,280,604,847,1819,2548,5464,7651,16399,22960,

%T 49204,68887,147619,206668,442864,620011,1328599,1860040,3985804,

%U 5580127,11957419,16740388,35872264,50221171,107616799,150663520,322850404

%N Partial sums of A162766.

%H Vincenzo Librandi, <a href="/A164265/b164265.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3).

%F a(n) = 3*a(n-2)+7 for n > 2; a(1) = 4, a(2) = 7.

%F a(n) = (11-4*(-1)^n)*3^(1/4*(2*n-1+(-1)^n))/2-7/2.

%F G.f.: x*(4+3*x)/((1-x)*(1-3*x^2)).

%t LinearRecurrence[{1,3,-3},{4,7,19},40] (* _Harvey P. Dale_, Aug 28 2016 *)

%o (Magma) T:=[ n le 2 select 5-n else 3*Self(n-2): n in [1..33] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

%o (PARI) a(n)=if(n%2,15,7)*3^(n\2)\2-3 \\ _Charles R Greathouse IV_, Jul 15 2011

%Y Cf. A162766, A164123 (partial sums of A162436).

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Aug 11 2009