A272850 a(n) = (n^2 + (n+1)^2)*(n^2 + (n+1)^2 + 2*n*(n+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

Author

Matthew Badley, May 07 2016

Keywords

• nonn
• easy

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).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

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

Programs

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

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)