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Partial sums of A048696.
2

%I #18 Feb 10 2017 00:50:13

%S 1,10,29,76,189,462,1121,2712,6553,15826,38213,92260,222741,537750,

%T 1298249,3134256,7566769,18267802,44102381,106472572,257047533,

%U 620567646,1498182833

%N Partial sums of A048696.

%H Reinhard Zumkeller, <a href="/A048772/b048772.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 (3,-1,-1).

%F a(n)=2*a(n-1)+a(n-2)+8; a(0)=1, a(1)=10.

%F a(n)=[ {(9+5*sqrt(2))(1+sqrt(2))^n - (9-5*sqrt(2))(1-sqrt(2))^n}/2*sqrt(2) ]-4.

%F a(0)=1, a(1)=10, a(2)=29, a(n)=3*a(n-1)-a(n-2)-a(n-3). - _Harvey P. Dale_, Apr 20 2012

%F G.f. ( 1+7*x ) / ( (x-1)*(x^2+2*x-1) ). a(n)=A048739(n)+7*A048739(n-1). - _R. J. Mathar_, Nov 08 2012

%t Accumulate[LinearRecurrence[{2,1},{1,9},30]] (* or *) LinearRecurrence[ {3,-1,-1},{1,10,29},30] (* _Harvey P. Dale_, Apr 20 2012 *)

%o (Haskell)

%o a048772 n = a048772_list !! n

%o a048772_list = scanl1 (+) a048696_list

%o -- _Reinhard Zumkeller_, Dec 15 2013

%o (PARI) a(n)=([0,1,0; 0,0,1; -1,-1,3]^n*[1;10;29])[1,1] \\ _Charles R Greathouse IV_, Feb 10 2017

%Y Cf. A001333, A000129, A048694-A048696, A105082.

%K easy,nice,nonn

%O 0,2

%A _Barry E. Williams_