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 A128416 Expansion of (1-4x^2)/(1+4x+3x^2). 2

%I #19 Mar 09 2022 03:31:39

%S 1,-4,9,-24,69,-204,609,-1824,5469,-16404,49209,-147624,442869,

%T -1328604,3985809,-11957424,35872269,-107616804,322850409,-968551224,

%U 2905653669,-8716961004,26150883009,-78452649024,235357947069,-706073841204,2118221523609

%N Expansion of (1-4x^2)/(1+4x+3x^2).

%C Diagonal sums of number triangle A128414.

%H Colin Barker, <a href="/A128416/b128416.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 (-4,-3).

%F G.f.: (1-4*x^2)/(1+4*x+3*x^2).

%F For n > 1, |a(n)| = 3*(|a(n-1)| - 1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Sep 17 2010

%F From _Colin Barker_, Sep 21 2016: (Start)

%F a(n) = (-1)^n*(9+5*3^n)/6 for n>0.

%F a(n) = -4*a(n-1)-3*a(n-2) for n>2. (End)

%o (PARI) Vec((1-4*x^2)/(1+4*x+3*x^2) + O(x^30)) \\ _Colin Barker_, Sep 21 2016

%Y Cf. A128414.

%K easy,sign

%O 0,2

%A _Paul Barry_, Mar 02 2007

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Last modified December 6 09:20 EST 2023. Contains 367600 sequences. (Running on oeis4.)