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%I #45 Feb 28 2024 15:58:44
%S 1,1,-5,-11,19,85,-29,-539,-365,2869,5059,-12155,-42509,30421,285475,
%T 102949,-1609901,-2227595,7431811,20797381,-23793485,-148577771,
%U -5816861,885649765,920550931,-4393347659,-9916653245,16443432709
%N Expansion of 1/(1-x*(1-6*x)).
%C Row sums of Riordan array (1, x(1-6x)).
%C For positive n, a(n) equals the determinant of the n X n tridiagonal matrix with 1's along the main diagonal, 3's along the superdiagonal, and 2's along the subdiagonal (see Mathematica code below). - _John M. Campbell_, Jul 08 2011
%H Seiichi Manyama, <a href="/A145934/b145934.txt">Table of n, a(n) for n = 0..2569</a>
%H Taras Goy and Mark Shattuck, <a href="https://doi.org/10.2478/amsil-2023-0027">Determinants of Toeplitz-Hessenberg Matrices with Generalized Leonardo Number Entries</a>, Ann. Math. Silesianae (2023). See p. 17.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-6).
%F a(n) = Sum_{k=0..n} A109466(n,k)*6^(n-k).
%F a(n) = a(n-1) - 6*a(n-2); a(0)=1, a(1)=1. - _Philippe Deléham_, Oct 25 2008
%t Table[Det[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 + 1]*2 + KroneckerDelta[#1, #2 - 1]*3 &, {n, n}]], {n, 1, 40}] (* _John M. Campbell_, Jul 08 2011 *)
%t LinearRecurrence[{1,-6}, {1,1}, 30] (* _G. C. Greubel_, Jan 14 2018 *)
%o (Sage) [lucas_number1(n,1,6) for n in range(1, 29)] # _Zerinvary Lajos_, Apr 22 2009
%o (PARI) Vec(1/(1-x*(1-6*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012
%o (Magma) I:=[1,1]; [n le 2 select I[n] else Self(n-1) - 6*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 14 2018
%Y Cf. A010892, A107920, A106852, A106853, A106854.
%K sign,easy
%O 0,3
%A _Philippe Deléham_, Oct 25 2008
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