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%I #18 Feb 08 2024 09:46:52
%S 2,17,149,1343,12401,116807,1117649,10823543,105764801,1040353607,
%T 10282475249,101977326743,1013841287201,10096889010407,
%U 100678223072849,1004747561509943,10033232930569601,100232630513987207,1001628413597910449,10011398895185373143
%N a(n) = 7^n + 10^n.
%H Vincenzo Librandi, <a href="/A245807/b245807.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-70).
%F G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
%F E.g.f.: e^(7*x) + e^(10*x).
%F a(n) = 17*a(n-1)-70*a(n-2).
%F a(n) = A000420(n) + A011557(n).
%t Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]
%o (Magma) [7^n+10^n: n in [0..25]]; /* or */ I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];
%Y Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Aug 04 2014
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