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a(n) = 10^n - 5^n.
1

%I #20 Nov 13 2024 17:15:43

%S 0,5,75,875,9375,96875,984375,9921875,99609375,998046875,9990234375,

%T 99951171875,999755859375,9998779296875,99993896484375,

%U 999969482421875,9999847412109375,99999237060546875,999996185302734375,9999980926513671875

%N a(n) = 10^n - 5^n.

%H G. C. Greubel, <a href="/A248340/b248340.txt">Table of n, a(n) for n = 0..995</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-50).

%F G.f.: 5*x/((1-5*x)*(1-10*x)).

%F a(n) = 15*a(n-1) - 50*a(n-2).

%F a(n) = 5^n*(2^n-1) = A000351(n) * A000225(n) = A011557(n) - A000351(n).

%F a(n) = 5*A016164(n-1).

%F a(n) = A016164(n) - A011557(n).

%F E.g.f.: exp(10*x) - exp(5*x). - _G. C. Greubel_, Nov 13 2024

%t Table[10^n - 5^n, {n,0,30}]

%t CoefficientList[Series[5 x/((1-5 x)(1-10 x)), {x, 0, 30}], x]

%o (Magma) [10^n-5^n: n in [0..30]];

%o (Python)

%o def A248340(n): return pow(10,n) - pow(5,n)

%o print([A248340(n) for n in range(41)]) # _G. C. Greubel_, Nov 13 2024

%Y Cf. sequences of the form k^n-5^n: A005062 (k=6), A121213 (k=7), A191468 (k=8), A191466 (k=9), this sequence (k=10), A139743 (k=11).

%Y Cf. A000225, A000351, A011557, A016164.

%K nonn,easy,changed

%O 0,2

%A _Vincenzo Librandi_, Oct 05 2014