A106330 Numbers k such that k^2 = 24*j^2 + 25.

5, 7, 11, 25, 59, 103, 245, 583, 1019, 2425, 5771, 10087, 24005, 57127, 99851, 237625, 565499, 988423, 2352245, 5597863, 9784379, 23284825, 55413131, 96855367, 230496005, 548533447, 958769291, 2281675225, 5429921339, 9490837543, 22586256245, 53750679943

Offset

1,1

Comments

The ratio k(n) /(2*j(n)) tends to sqrt(6) as n increases.

k(n) = 2*b + 1, for n > 0, where b is a side of the Heronian triangle (5, b, b+1). - Andrés Ventas, Dec 13 2024

Links

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (0,0,10,0,0,-1).

Formula

Recurrence: k(1)=5, k(2)=7, k(3)=11, k(4)=25, k(5)=10*k(2)-k(3), k(6)=10*k(3)-k(2) then k(n)=10*k(n-3)-k(n-6).

From Ralf Stephan, Nov 15 2010: (Start)

G.f.: (-7x^5-11x^4-25x^3+11x^2+7x+5)/(x^6-10x^3+1).

a(3n+1) = 5*A001079(n), a(3n+2) = A077409(n), a(3n+3) = A077250(n). (End)

Prog

(PARI) Vec(-x*(7*x^5+11*x^4+25*x^3-11*x^2-7*x-5)/(x^6-10*x^3+1) + O(x^100)) \\ Colin Barker, Apr 16 2014

Crossrefs

Cf. A106331.

Sequence in context: A067289 A036491 A036490 * A057247 A157437 A213677

Adjacent sequences: A106327 A106328 A106329 * A106331 A106332 A106333

Keyword

nonn,easy

Author

Pierre CAMI, Apr 29 2005

Extensions

More terms from Ralf Stephan, Nov 15 2010

More terms from Colin Barker, Apr 16 2014

Status

approved