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

1,1

Links

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

Formula

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

Example

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}}.

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

Prog

(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

Crossrefs

Partial sums of A267326.

Cf. A000118, A046897.

Sequence in context: A081654 A307004 A264280 * A253105 A290915 A334693

Adjacent sequences: A264387 A264388 A264389 * A264391 A264392 A264393

Keyword

nonn,easy

Author

Christopher Heiling, Jan 12 2016

Status

approved