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%I #14 Feb 27 2019 12:29:40
%S 1,1,2,5,7,12,31,43,74,191,265,456,1177,1633,2810,7253,10063,17316,
%T 44695,62011,106706,275423,382129,657552,1697233,2354785,4052018,
%U 10458821,14510839,24969660,64450159,89419819,153869978,397159775,551029753,948189528,2447408809,3395598337,5843007146
%N Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1.
%C The numerators are given in A295333. There details are given.
%H Robert Israel, <a href="/A295334/b295334.txt">Table of n, a(n) for n = 0..3795</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 6, 0, 0, 1).
%F G.f.: G(x) = (1 + x + 2*x^2 - x^3 + x^4)/(1 - 6*x^3 - x^6), For the derivation see A295333, but here the input of the recurrence is a(0) = 1, a(-1) = 0 (a(-2) = a(0) = 1). This leads here to G_0 = 1+ 2*x*G_2 + x*G_1, G_1 = G_0 + x*G_2, G_2 = G_1 + G_0 and the solution gives G(x).
%F a(n) = 6*a(n-3) + a(n-6), n >= 6, with inputs a(0)..a(5).
%e For the first convergents see A295333.
%p numtheory:-cfrac(sqrt(5/2),100,'con'):
%p map(denom,con[1..-2]); # _Robert Israel_, Nov 22 2017
%t Denominator[Convergents[Sqrt[5/2], 50]] (* _Wesley Ivan Hurt_, Nov 21 2017 *)
%Y Cf. A020797, A295333.
%K nonn,frac,cofr,easy
%O 0,3
%A _Wolfdieter Lang_, Nov 21 2017