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A272850
a(n) = (n^2 + (n+1)^2)*(n^2 + (n+1)^2 + 2*n*(n+1)).
1
1, 45, 325, 1225, 3321, 7381, 14365, 25425, 41905, 65341, 97461, 140185, 195625, 266085, 354061, 462241, 593505, 750925, 937765, 1157481, 1413721, 1710325, 2051325, 2440945, 2883601, 3383901, 3946645, 4576825, 5279625
OFFSET
0,2
COMMENTS
Larger of pair of integers whose Pythagorean means are all integers.
The smaller of the pairs are: (A001844).
The arithmetic means are: (A007204)
The geometric means are: (A005917)
The harmonic means are: (A016754).
Subtracting terms in A016754 from A007204 gives complementary harmonics (A060300).
FORMULA
a(n) = (2*n^2 + 2*n + 1)*(4*n^2 + 4*n + 1).
From Colin Barker, May 24 2016: (Start)
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4.
G.f.: (1 + 40*x + 110*x^2 + 40*x^3 + x^4) / (1-x)^5. (End)
PROG
(PARI) a(n)=8*n^4 + 16*n^3 + 14*n^2 + 6*n + 1 \\ Charles R Greathouse IV, May 23 2016
(PARI) Vec((1+40*x+110*x^2+40*x^3+x^4)/(1-x)^5 + O(x^50)) \\ Colin Barker, May 24 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Matthew Badley, May 07 2016
STATUS
approved