A272850 - OEIS

%I #19 May 25 2016 08:53:52

%S 1,45,325,1225,3321,7381,14365,25425,41905,65341,97461,140185,195625,

%T 266085,354061,462241,593505,750925,937765,1157481,1413721,1710325,

%U 2051325,2440945,2883601,3383901,3946645,4576825,5279625

%N a(n) = (n^2 + (n+1)^2)*(n^2 + (n+1)^2 + 2*n*(n+1)).

%C Larger of pair of integers whose Pythagorean means are all integers.

%C The smaller of the pairs are: (A001844).

%C The arithmetic means are: (A007204)

%C The geometric means are: (A005917)

%C The harmonic means are: (A016754).

%C Subtracting terms in A016754 from A007204 gives complementary harmonics (A060300).

%H Seiichi Manyama, <a href="/A272850/b272850.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (2*n^2 + 2*n + 1)*(4*n^2 + 4*n + 1).

%F From _Colin Barker_, May 24 2016: (Start)

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4.

%F G.f.: (1 + 40*x + 110*x^2 + 40*x^3 + x^4) / (1-x)^5. (End)

%o (PARI) a(n)=8*n^4 + 16*n^3 + 14*n^2 + 6*n + 1 \\ _Charles R Greathouse IV_, May 23 2016

%o (PARI) Vec((1+40*x+110*x^2+40*x^3+x^4)/(1-x)^5 + O(x^50)) \\ _Colin Barker_, May 24 2016

%Y Cf. A001844, A007204, A005917, A016754, A060300.

%K nonn,easy

%O 0,2

%A _Matthew Badley_, May 07 2016