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%I #15 Sep 08 2022 08:45:38
%S 1,7,56,490,4508,42532,406112,3899224,37532432,361686640,3487250816,
%T 33630672544,324364881344,3128620091968,30177356271104,
%U 291080943932800,2807684251672832,27082179878242048,261227779725129728
%N a(n) = ((7 + sqrt(7))^n + (7 - sqrt(7))^n)/2.
%C Binomial transform is A152265, inverse binomial transform is A146966.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14, -42).
%F From _R. J. Mathar_, Oct 10 2008: (Start)
%F a(n) = 14*a(n-1) - 42*a(n-2).
%F G.f.: (1-7x)/(1-14x+42x^2). (End)
%F a(n) = Sum_{k=0..n} 7^k*A098158(n,k). - _Philippe Deléham_, Oct 14 2008
%o (Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((7+r7)^n+(7-r7)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Oct 20 2008, Jul 09 2009
%Y Cf. A098158, A152265, A146966.
%K nonn
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008
%E More terms from _R. J. Mathar_, Oct 10 2008
%E Edited by _Klaus Brockhaus_, Jul 09 2009
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