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A245923 G.f.: (1-x + sqrt(1 - 14*x + x^2)) / (2*(1 - 14*x + x^2)). 3

%I #12 Jan 30 2020 21:29:17

%S 1,10,127,1684,22717,309214,4231675,58117672,800173945,11037041074,

%T 152448280183,2107959984316,29172777600565,404016491894662,

%U 5598523988234227,77617624970307664,1076533162210721521,14936507761662251866,207302489038473478255,2877906561872502533860

%N G.f.: (1-x + sqrt(1 - 14*x + x^2)) / (2*(1 - 14*x + x^2)).

%C Self-convolution of A245926.

%C Limit a(n+1)/a(n) = 7 + 4*sqrt(3).

%H G. C. Greubel, <a href="/A245923/b245923.txt">Table of n, a(n) for n = 0..870</a>

%F a(n) ~ (7+4*sqrt(3))^(n+1) * (2-sqrt(3))/8 * (1+1/(3^(1/4)*sqrt(Pi*n/2))). - _Vaclav Kotesovec_, Aug 17 2014

%F D-finite with recurrence: n*a(n) +7*(-4*n+3)*a(n-1) +99*(2*n-3)*a(n-2) +7*(-4*n+9)*a(n-3) +(n-3)*a(n-4)=0. - _R. J. Mathar_, Jan 23 2020

%e G.f.: A(x) = 1 + 10*x + 127*x^2 + 1684*x^3 + 22717*x^4 + 309214*x^5 +...

%t CoefficientList[Series[(1 - x + Sqrt[1 - 14*x + x^2])/(2*(1 - 14*x + x^2)), {x,0,50}], x] (* _G. C. Greubel_, Feb 14 2017 *)

%o (PARI) {a(n)=polcoeff( (1-x + sqrt(1-14*x+x^2 +x*O(x^n))) / (2*(1-14*x+x^2 +x*O(x^n))), n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A245924, A245926.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 16 2014

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)