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Third binomial transform of Pell(3*n)/Pell(3).
2

%I #14 Aug 04 2021 16:18:20

%S 0,1,20,350,6000,102500,1750000,29875000,510000000,8706250000,

%T 148625000000,2537187500000,43312500000000,739390625000000,

%U 12622187500000000,215474218750000000,3678375000000000000

%N Third binomial transform of Pell(3*n)/Pell(3).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-50).

%F G.f.: x/(1-20*x+50*x^2);

%F a(n) = ((10 + 5*sqrt(2))^n - (10 - 5*sqrt(2))^n)/(10*sqrt(2)).

%t LinearRecurrence[{20,-50},{0,1},30] (* _Harvey P. Dale_, Aug 04 2021 *)

%Y Cf. A000129, A041085.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Mar 26 2004