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A253674 Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448). 3


%S 1,10,40,931,3871,91180,379270,8934661,37164541,875505550,3641745700,

%T 85790609191,356853914011,8406604195120,34968041827330,

%U 823761420512521,3426511245164281,80720212606031890,335763133984272160,7909757073970612651,32901360619213507351

%N Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448).

%C Also positive integers y in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of x being A253673.

%H Colin Barker, <a href="/A253674/b253674.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,98,-98,-1,1).

%F a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^2-5*x+1)*(x^2+14*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

%e 10 is in the sequence because the 10th centered octagonal number is 361, which is also the 16th centered triangular number.

%t LinearRecurrence[{1,98,-98,-1,1},{1,10,40,931,3871},30] (* _Harvey P. Dale_, Oct 01 2015 *)

%o (PARI) Vec(-x*(x^2-5*x+1)*(x^2+14*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

%Y Cf. A005448, A016754, A253673, A253675.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 08 2015

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Last modified January 23 14:45 EST 2021. Contains 340385 sequences. (Running on oeis4.)