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a(n) = 5*a(n-2) + 2, a(0) = 1, a(1) = 2.
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%I #15 Jul 18 2024 14:47:49

%S 1,2,7,12,37,62,187,312,937,1562,4687,7812,23437,39062,117187,195312,

%T 585937,976562,2929687,4882812,14648437,24414062,73242187,122070312,

%U 366210937,610351562,1831054687,3051757812,9155273437,15258789062,45776367187,76293945312

%N a(n) = 5*a(n-2) + 2, a(0) = 1, a(1) = 2.

%C Row sums of triangle in A152717.

%H Harvey P. Dale, <a href="/A238366/b238366.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 (1,5,-5).

%F G.f.: (1+x)/((1-x)*(1-5*x^2)).

%F a(n) = Sum_{k=0..n} A152717(n,k).

%F a(2*n) = A057651(n).

%F a(2*n+1) = A125831(n+1) = 2*A003463(n+1).

%F a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3), a(0) = 1, a(1) = 2, a(2) = 7.

%F a(n) = A198306(n+1) for n > 1. - _Georg Fischer_, Oct 23 2018

%t LinearRecurrence[{1,5,-5},{1,2,7},40] (* _Harvey P. Dale_, Jul 18 2024 *)

%Y Cf. A057651, A125831, A152717, A198306.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Feb 25 2014