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A253822 Indices of centered triangular numbers (A005448) which are also octagonal numbers (A000567). 3


%S 1,256,833,294848,960705,340253760,1108652161,392652543616,

%T 1279383632513,453120695078528,1476407603267265,522900889468077120,

%U 1703773094786790721,603427173325465917376,1966152674976353224193,696354435116698200574208,2268938483149616833927425

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

%C Also positive integers y in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of x being A253821.

%H Colin Barker, <a href="/A253822/b253822.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*(255*x^3+577*x^2-255*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

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

%t LinearRecurrence[{1,1154,-1154,-1,1},{1,256,833,294848,960705},20] (* _Harvey P. Dale_, Jul 19 2019 *)

%o (PARI) Vec(x*(255*x^3+577*x^2-255*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

%Y Cf. A000567, A005448, A253821, A253823.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 14 2015

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)