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A182780 Twice A024537. 4

%I #27 Sep 08 2022 08:45:55

%S 2,4,8,18,42,100,240,578,1394,3364,8120,19602,47322,114244,275808,

%T 665858,1607522,3880900,9369320,22619538,54608394,131836324,318281040,

%U 768398402,1855077842,4478554084,10812186008,26102926098,63018038202,152139002500,367296043200,886731088898,2140758220994,5168247530884

%N Twice A024537.

%C a(n) = A078057(n) + 1 (see A288213). - _Michel Dekking_, Sep 29 2019

%H Colin Barker, <a href="/A182780/b182780.txt">Table of n, a(n) for n = 0..1000</a>

%H J. V. Leyendekkers and A. G. Shannon, <a href="http://nntdm.net/volume-18-2012/number-2/58-62/">Pellian sequence relationships among pi, e, sqrt(2)</a>, Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 58-62. See Table 2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1).

%F From _Colin Barker_, May 26 2018: (Start)

%F G.f.: 2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)).

%F a(n) = (2 + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.

%F a(n) = 3*a(n-1) - a(n-2) - a(n-3) for n>2.

%F (End)

%o (PARI) Vec(2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)) + O(x^40)) \\ _Colin Barker_, May 26 2018

%o (Magma) a:=[2,4,8]; [n le 3 select a[n] else 3*Self(n-1) - Self(n-2) - Self(n-3):n in [1..35]]; // _Marius A. Burtea_, Sep 29 2019

%Y Cf. A024537.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Dec 23 2012

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Last modified March 28 14:02 EDT 2024. Contains 371254 sequences. (Running on oeis4.)