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A254711 Pentagonal numbers (A000326) which are also centered square numbers (A001844). 3

%I #5 Jun 13 2015 00:55:24

%S 1,5,145,925,28085,179401,5448301,34802825,1056942265,6751568605,

%T 205041351065,1309769506501,39776965164301,254088532692545,

%U 7716526200523285,49291865572847185,1496966305936352945,9562367832599661301,290403746825451948001

%N Pentagonal numbers (A000326) which are also centered square numbers (A001844).

%H Colin Barker, <a href="/A254711/b254711.txt">Table of n, a(n) for n = 1..875</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,194,-194,-1,1).

%F a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+4*x^3-54*x^2+4*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).

%e 145 is in the sequence because it is the 10th pentagonal number and the 9th centered square number.

%o (PARI) Vec(-x*(x^4+4*x^3-54*x^2+4*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

%Y Cf. A000326, A001844, A254709, A254710.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Feb 06 2015

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