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Denominators of (1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n)), n >= 0.
1

%I #9 Mar 18 2018 09:40:05

%S 1,28,280,520,416,608,1672,2200,700,217,4216,5032,2960,3440,7912,9016,

%T 1274,2860,12760,14152,7808,8576,18760,20440,5548,3002,25912,27880,

%U 14960,16016,34216,36472,2425,10300,43672,46216,24416,25760

%N Denominators of (1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n)), n >= 0.

%C The numerators are given in A300296, where details and the Jolley reference are given.

%F a(n) = denominator(r(n)), with r(n) = n*(5 + 3*n)/(8*(1 + 3*n)*(4 + 3*n)).

%F a(n) = (1 + 3*n)*(4 + 3*n)/4 if n == 0 or 9 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n)/2 if n == 16 or 25 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n) if n == 1 or 8 or 17 or 24 (mod 32), and for other n one has a(n) = 2*(1 + 3*n)*(4 + 3*n) if n == 0 or 1 (mod 4) and a(n) = 4*(1 + 3*n)*(4 + 3*n) if n == 2 or 3 (mod 4).

%F G.f.: G(x) = (1/24)*(1 - hypergeometric([1, 2], [7/3], -x/(1-x)))/(1-x).

%e For the first rationals r(n) see A300296.

%o (PARI) a(n) = denominator((1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n))); \\ _Altug Alkan_, Mar 18 2018

%Y Cf. A300296.

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Mar 17 2018