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A254230 Heptagonal numbers (A000566) which are also centered square numbers (A001844). 3


%S 1,4141,85285,429332905,8842505113,44514094237813,916808615026525,

%T 4615310318335580305,95056550814337645681,478524604381155542930941,

%U 9855653300615347164456661,49614388026831658683830230201,1021853845419343873890857865865

%N Heptagonal numbers (A000566) which are also centered square numbers (A001844).

%H Colin Barker, <a href="/A254230/b254230.txt">Table of n, a(n) for n = 1..399</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,103682,-103682,-1,1).

%F a(n) = a(n-1)+103682*a(n-2)-103682*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+4140*x^3-22538*x^2+4140*x+1) / ((x-1)*(x^2-322*x+1)*(x^2+322*x+1)).

%e 4141 is in the sequence because it is the 41st heptagonal number and the 46th centered square number.

%o (PARI) Vec(-x*(x^4+4140*x^3-22538*x^2+4140*x+1)/((x-1)*(x^2-322*x+1)*(x^2+322*x+1)) + O(x^100))

%Y Cf. A000566, A001844, A254228, A254229.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 27 2015

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)