A196508 - OEIS

%I #21 Apr 04 2024 09:49:45

%S 0,4,20,76,252,764,2172,5884,15356,38908,96252,233468,557052,1310716,

%T 3047420,7012348,15990780,36175868,81264636,181403644,402653180,

%U 889192444,1954545660,4278190076,9328132092,20266876924,43889197052

%N a(n) = 2^n*(n^2 - n + 4)-4.

%D Jolley, Summation of Series, Dover (1961), eq. (46) on page 8.

%H Vincenzo Librandi, <a href="/A196508/b196508.txt">Table of n, a(n) for n = 0..3000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8)

%F a(n) = 2*2 + 4*4 + 7*8 + 11*16 + 16*32 + ... (n terms of A000124*A000079).

%F a(n) = 4*A053545(n).

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

%o (Magma) [2^n*(n^2-n+4)-4: n in [0..30]]; // _Vincenzo Librandi_, Oct 05 2011

%K nonn,easy

%O 0,2

%A _R. J. Mathar_, Oct 03 2011