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%I #20 Jul 09 2022 11:11:10
%S 1,253,64261,16322041,4145734153,1053000152821,267457893082381,
%T 67933251842771953,17254778510170993681,4382645808331589623021,
%U 1113174780537713593253653,282742011610770921096804841,71815357774355276244995175961,18240818132674629395307677889253
%N Triangular numbers (A000217) that are also centered heptagonal numbers (A069099).
%H Colin Barker, <a href="/A253880/b253880.txt">Table of n, a(n) for n = 1..416</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (254,-1).
%F a(n) = 254*a(n-1) - a(n-2).
%F G.f.: -x*(x-1) / (x^2 - 254*x + 1).
%F a(n) = (1/8)*T(2*n-1, 8), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - _Peter Bala_, Jul 08 2022
%e 253 is in the sequence because it is the 22nd triangular number and the 9th centered heptagonal number.
%t LinearRecurrence[{254,-1},{1,253},20] (* _Harvey P. Dale_, May 17 2017 *)
%o (PARI) Vec(-x*(x-1)/(x^2-254*x+1) + O(x^100))
%Y Cf. A000217, A069099, A253878, A253879.
%Y Similar sequences of the type cosh((2*m+1)*arccosh(k))/k are listed in A302329. This is the case k=8.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 17 2015