A300297 Denominators of (1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n)), n >= 0.

1, 28, 280, 520, 416, 608, 1672, 2200, 700, 217, 4216, 5032, 2960, 3440, 7912, 9016, 1274, 2860, 12760, 14152, 7808, 8576, 18760, 20440, 5548, 3002, 25912, 27880, 14960, 16016, 34216, 36472, 2425, 10300, 43672, 46216, 24416, 25760

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..37.

Formula

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

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).

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

Example

For the first rationals r(n) see A300296.

Prog

(PARI) a(n) = denominator((1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n))); \\ Altug Alkan, Mar 18 2018

Crossrefs

Cf. A300296.

Sequence in context: A159883 A125391 A126549 * A250649 A107418 A183484

Adjacent sequences: A300294 A300295 A300296 * A300298 A300299 A300300

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Mar 17 2018

Status

approved