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A254228 Indices of heptagonal numbers (A000566) which are also centered square numbers (A001844). 3

%I #7 Jun 13 2015 00:55:22

%S 1,41,185,13105,59473,4219673,19150025,1358721505,6166248481,

%T 437504104841,1985512860761,140874963037201,639328974916465,

%U 45361300593873785,205861944410240873,14606197916264321473,66286906771122644545,4703150367736517640425

%N Indices of heptagonal numbers (A000566) which are also centered square numbers (A001844).

%C Also positive integers x in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of y being A254229.

%H Colin Barker, <a href="/A254228/b254228.txt">Table of n, a(n) for n = 1..797</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).

%F a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+40*x^3-178*x^2+40*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).

%e 41 is in the sequence because the 41st heptagonal number is 4141, which is also the 46th centered square number.

%o (PARI) Vec(-x*(x^4+40*x^3-178*x^2+40*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))

%Y Cf. A000566, A001844, A254229, A254230.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 27 2015

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