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a(n)=5n^2+20n+4.
1

%I #10 Jun 17 2017 04:36:48

%S 29,64,109,164,229,304,389,484,589,704,829,964,1109,1264,1429,1604,

%T 1789,1984,2189,2404,2629,2864,3109,3364,3629,3904,4189,4484,4789,5104

%N a(n)=5n^2+20n+4.

%C Most quintic polynomials x^5 + 5x(5*n^2+20n+4) + 8(5*n^2+20n+4) (with the exception of n=0 or 4 when the polynomial is solvable, or n=-2 when it is reducible) have nonsolvable alternating Galois group A_5 (of order 60) over rational numbers.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

%F G.f.: -x*(29-23*x+4*x^2)/(-1+x)^3. - _R. J. Mathar_, Nov 14 2007

%t Table[5n^2 + 20n + 4, {n, 1, 30}]

%o (PARI) a(n)=5*n^2+20*n+4 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A134538.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Oct 31 2007, Nov 21 2007