%I #13 Oct 15 2025 14:24:02

%S 1,3,10,35,126,461,1702,6315,23494,87533,326382,1217483,4542526,

%T 16950573,63255670,236063915,880983606,3287837741,12270301822,

%U 45793238475,170902389934,637815796973,2380359749382,8883621103403,33154120469926,123732852387693,461777272303630

%N Expansion of (1-3x+x^2)/((1-2x)(1-4x+x^2)).

%C Binomial transform of A057960.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,2).

%F a(0)=1, a(1)=3, a(2)=10, a(n)=6a(n-1)-9a(n-2)+2a(n-3), n>2.

%F a(n) = 2^n/3+(2+sqrt(3))(2+sqrt(3))^n/6+(2-sqrt(3))(2-sqrt(3))^n/6.

%F a(n) = A087944(n+1)/2.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 16 2003