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A103715
Define a(1)=0, a(2)=0, a(3)=1, a(4)=3, a(5)=18, a(6)=22, a(7)=119, a(8)=285. Then a(n) = a(n-8) + 4*sqrt(420*a(n-4)^2 + 420*a(n-4) + 1).
1
0, 0, 1, 3, 18, 22, 119, 285, 1516, 1844, 9797, 23407, 124334, 151226, 803275, 1919129, 10193912, 12398728, 65858793, 157345211, 835776490, 1016544510, 5399617791, 12900388213, 68523478308, 83344251132, 442702800109
OFFSET
1,4
COMMENTS
By construction, a(n) is an integer so 420*a(n)^2 + 420*a(n) + 1 = j(n)^2. The sequence j(n) starts: 1, 1, 29, 71, 379, 461, 2449, 5851, ...
LINKS
FORMULA
From R. J. Mathar, Nov 13 2009: (Start)
a(n) = a(n-1) + 82*a(n-4) - 82*a(n-5) - a(n-8) + a(n-9).
G.f.: x^3*(x^2+1)*(x^4+2*x^3+14*x^2+2*x+1)/((1-x)*(x^8-82*x^4+1)). (End)
MATHEMATICA
Rest[CoefficientList[Series[x^3*(x^2+1)*(x^4+2*x^3+14*x^2+2*x+1)/((1-x)*(x^8-82*x^4+1)), {x, 0, 30}], x]] (* G. C. Greubel, Jul 15 2018 *)
PROG
(PARI) x='x+O('x^30); concat([0, 0], Vec(x^3*(x^2+1)*(x^4+2*x^3+14*x^2 +2*x +1)/((1-x)*(x^8-82*x^4+1)))) \\ G. C. Greubel, Jul 15 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0, 0] cat Coefficients(R!(x^3*(x^2+1)*(x^4+2*x^3+14*x^2+2*x+1)/((1-x)*(x^8- 82*x^4 +1)))); // G. C. Greubel, Jul 15 2018
CROSSREFS
Sequence in context: A291167 A361592 A174029 * A131860 A346421 A263578
KEYWORD
nonn,easy
AUTHOR
Pierre CAMI, Mar 27 2005
EXTENSIONS
Extended by R. J. Mathar, Nov 13 2009
STATUS
approved