This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295334 #14 Feb 27 2019 12:29:40 %S A295334 1,1,2,5,7,12,31,43,74,191,265,456,1177,1633,2810,7253,10063,17316, %T A295334 44695,62011,106706,275423,382129,657552,1697233,2354785,4052018, %U A295334 10458821,14510839,24969660,64450159,89419819,153869978,397159775,551029753,948189528,2447408809,3395598337,5843007146 %N A295334 Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1. %C A295334 The numerators are given in A295333. There details are given. %H A295334 Robert Israel, <a href="/A295334/b295334.txt">Table of n, a(n) for n = 0..3795</a> %H A295334 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 6, 0, 0, 1). %F A295334 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 A295334 a(n) = 6*a(n-3) + a(n-6), n >= 6, with inputs a(0)..a(5). %e A295334 For the first convergents see A295333. %p A295334 numtheory:-cfrac(sqrt(5/2),100,'con'): %p A295334 map(denom,con[1..-2]); # _Robert Israel_, Nov 22 2017 %t A295334 Denominator[Convergents[Sqrt[5/2], 50]] (* _Wesley Ivan Hurt_, Nov 21 2017 *) %Y A295334 Cf. A020797, A295333. %K A295334 nonn,frac,cofr,easy %O A295334 0,3 %A A295334 _Wolfdieter Lang_, Nov 21 2017