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A251625 Numbers n such that the octagonal number N(n) is the sum of three consecutive octagonal numbers. 2

%I

%S 483,1304163,3523847043,9521433405123,25726909536794403,

%T 69514100046985070883,187827072600044124730563,

%U 507508680651219178036909443,1371288267292521619011604583523,3705220390715712763350177547768803,10011504124425588594050560722466721283

%N Numbers n such that the octagonal number N(n) is the sum of three consecutive octagonal numbers.

%C Also nonnegative integers y in the solutions to 18*x^2-6*y^2+24*x+4*y+18 = 0, the corresponding values of x being A251624.

%C It seems that the least significant digit of each term is 3.

%H Colin Barker, <a href="/A251625/b251625.txt">Table of n, a(n) for n = 1..291</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2703,-2703,1).

%F a(n) = 2703*a(n-1)-2703*a(n-2)+a(n-3).

%F G.f.: -3*x*(x^2-462*x+161) / ((x-1)*(x^2-2702*x+1)).

%F a(n) = (1 + 2*(sqrt(3)+2)*(1351+780*sqrt(3))^(-n) - 2*(sqrt(3)-2)*(1351+780*sqrt(3))^n) / 3. - _Colin Barker_, May 30 2017

%e 483 is in the sequence because N(483) = 698901 = 231296+232965+234640 = N(278)+N(279)+N(280).

%o (PARI) Vec(-3*x*(x^2-462*x+161)/((x-1)*(x^2-2702*x+1)) + O(x^100))

%Y Cf. A000567, A251624.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Dec 06 2014

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Last modified March 8 06:23 EST 2021. Contains 341941 sequences. (Running on oeis4.)