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%I #22 Sep 08 2022 08:45:46
%S 2,7,22,72,232,752,2432,7872,25472,82432,266752,863232,2793472,
%T 9039872,29253632,94666752,306348032,991363072,3208118272,10381688832,
%U 33595850752,108718456832,351820316672,1138514460672,3684310188032
%N a(n) = ((2+sqrt(5))*(1+sqrt(5))^n + (2-sqrt(5))*(1-sqrt(5))^n)/2.
%C Binomial transform of A162963. Inverse binomial transform of A001077 without initial 1.
%H Michael De Vlieger, <a href="/A162770/b162770.txt">Table of n, a(n) for n = 0..1960</a>
%H Silvana Ramaj, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=3464&context=etd">New Results on Cyclic Compositions and Multicompositions</a>, Master's Thesis, Georgia Southern Univ., 2021. See p. 35.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,4).
%F a(n) = 2*a(n-1) + 4*a(n-2) for n > 1; a(0) = 2, a(1) = 7.
%F G.f.: (2+3*x)/(1-2*x-4*x^2).
%F a(n) = 2^(n-1) * A000032(n+3). - _Diego Rattaggi_, Jun 24 2020
%t LinearRecurrence[{2,4},{2,7},30] (* _Harvey P. Dale_, Jan 13 2015 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(1+r)^n+(2-r)*(1-r)^n)/2: n in [0..24] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 19 2009
%Y Cf. A000032, A001077, A162963.
%K nonn
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 19 2009
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