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%I #11 Aug 03 2021 20:28:01
%S 1,547,368551,248402701,167423051797,112842888508351,
%T 76055939431576651,51261590333994154297,34550235829172628419401,
%U 23286807687272017560521851,15695273830985510663163308047,10578591275276546914954509101701,7129954824262561635168675971238301
%N Centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
%H Colin Barker, <a href="/A253546/b253546.txt">Table of n, a(n) for n = 1..354</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (675,-675,1).
%F a(n) = 675*a(n-1)-675*a(n-2)+a(n-3).
%F G.f.: -x*(x^2-128*x+1) / ((x-1)*(x^2-674*x+1)).
%e 547 is in the sequence because it is the 14th centered hexagonal number and the 13th centered heptagonal number.
%t LinearRecurrence[{675,-675,1},{1,547,368551},20] (* _Harvey P. Dale_, Aug 03 2021 *)
%o (PARI) Vec(-x*(x^2-128*x+1) / ((x-1)*(x^2-674*x+1)) + O(x^100))
%Y Cf. A003215, A069099, A253457, A253458.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 03 2015