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A253821 Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448). 3


%S 1,181,589,208489,679321,240595741,783935461,277647276241,

%T 904660842289,320404716185989,1043977828065661,369746764831354681,

%U 1204749508926930121,426687446210667115501,1390279889323849293589,492396943180345019933089,1604381787530213157871201

%N Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448).

%C Also positive integers x in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of y being A253822.

%H Colin Barker, <a href="/A253821/b253821.txt">Table of n, a(n) for n = 1..653</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1154,-1154,-1,1).

%F a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+180*x^3-746*x^2+180*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

%e 181 is in the sequence because the 181st octagonal number is 97921, which is also the 256th centered triangular number.

%o (PARI) Vec(-x*(x^4+180*x^3-746*x^2+180*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

%Y Cf. A000567, A005448, A253822, A253823.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 14 2015

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Last modified September 28 04:28 EDT 2022. Contains 357063 sequences. (Running on oeis4.)