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A105051 Define a(1)=0, a(2)=0, a(3)=15, a(4)=111 then a(n)=254*a(n-2)+126-a(n-4) also sequence such that 7*(a(n)^2) + 7*a(n) + 1 = a square. 0
0, 0, 15, 111, 3936, 28320, 999855, 7193295, 253959360, 1827068736, 64504677711, 464068265775, 16383934179360, 117871512438240, 4161454776879855, 29938900091047311, 1056993129393303936, 7604362751613578880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence is such that 7*(a(n)^2) + 7*a(n) + 1 = j^2 = a square integer positive root of a(n)^2 + a(n) - (j^2-1)/7 = 0 is such that 2*a(n)+1=sqrt((4*j^2+3)/7), ((4*j^2+3)/7) need to be a square so j^2 = (7*k^2-3)/4, put k=2*a(n)+1 you found that (7*k^2-3)/4 = 7*(a(n)^2) + 7*a(n) + 1

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(n)=A105040(n-2). G.f.: 3x^2(5+32x+5x^2)/((1-x)(1+16x+x^2)(1-16x+x^2)). [From R. J. Mathar, Aug 28 2008]

CROSSREFS

Sequence in context: A034184 A092646 A222117 * A105040 A298123 A295384

Adjacent sequences:  A105048 A105049 A105050 * A105052 A105053 A105054

KEYWORD

nonn

AUTHOR

Pierre CAMI, Apr 04 2005

EXTENSIONS

Extended by R. J. Mathar, Aug 28 2008

STATUS

approved

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Last modified February 23 05:29 EST 2020. Contains 332159 sequences. (Running on oeis4.)