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%I #15 Jun 29 2023 23:52:41
%S 1,7,57,511,4817,46487,453321,4440527,43581217,428075431,4206226137,
%T 41336073247,406249753841,3992717550647,39241805801577,
%U 385683861645551,3790660025173057,37256202024955207,366169767317277561
%N a(n) = ((7 + sqrt(8))^n + (7 - sqrt(8))^n)/2.
%H Harvey P. Dale, <a href="/A147689/b147689.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 (14, -41).
%F From _Philippe Deléham_, Nov 13 2008: (Start)
%F a(n) = 14*a(n-1) - 41*a(n-2), a(0)=1, a(1)=7.
%F G.f.: (1-7x)/(1-14x+41x^2).
%F a(n) = (Sum_{k=0..n} A098158(n,k)*7^(2k)*8^(n-k))/7^n. (End)
%t LinearRecurrence[{14,-41},{1,7},20] (* _Harvey P. Dale_, Sep 11 2020 *)
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((7+r8)^n+(7-r8)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Nov 13 2008
%K nonn
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008
%E Extended beyond a(6) by _Klaus Brockhaus_, Nov 13 2008
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