A264390 Partial sums of A267326.

8, 32, 136, 160, 408, 720, 1176, 1200, 2168, 2912, 3976, 4288, 5752, 7120, 10344, 10368, 12824, 15728, 18776, 19520, 25448, 28640, 33064, 33376, 39624, 44016, 52760, 54128, 61096, 70768, 78712, 78736, 92568, 99936, 114072, 116976, 128232, 137376, 156408

Offset: 1

Author

Christopher Heiling, Jan 12 2016

Keywords

• nonn
• easy

Examples

			For n = 2 the a(n) = 32 integral solutions of x^2 + y^2 + z^2 + t^2 <= 2^2 are: {x,y,z,t} = {{0,0,0,1}; {0,0,1,0}; {0,1,0,0}; {1,0,0,0}; {0,0,0,-1}; {0,0,-1,0}; {0,-1,0,0}; {-1,0,0,0}; {0,0,0,2}; {0,0,0,-2}; {0,0,2,0}; {0,0,-2,0}; {0,2,0,0}; {0,-2,0,0}; {2,0,0,0}; {-2,0,0,0}; {1,1,1,1}; {1,1,1,-1}; {1,1,-1,1}; {1,-1,1,1}; {-1,1,1,1}; {1,1,-1,-1}; {1,-1,1,-1}; {-1,1,1,-1}; {1,-1,-1,1}; {-1,1,-1,1}; {1,-1,-1,-1}; {-1,1,-1,-1}; {-1,-1,1,-1}; {-1,-1,1,-1}; {-1,-1,-1,1}; {-1,-1,-1,-1}}.
		

Links

• Christopher Heiling, Table of n, a(n) for n = 1..150

Crossrefs

Partial sums of A267326.

Cf. A000118, A046897.

Programs

Maple

#A264390
terms := 42:
(add(q^(m^2), m = -terms..terms))^4:
seq(add(coeff(%, q, k^2), k = 1..n), n = 1..terms); # Peter Bala, Jan 15 2016

PARI

a000118(k) = if(k<1, k==0, 8 * sumdiv( k, d, if( d%4, d)));
a(n) = sum(k=1, n, a000118(k^2)); \\ Altug Alkan, Jan 19 2016

Formula

a(n) = Sum_{k = 1..n} A000118(k^2).