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A264390 Partial sums of A267326. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A200153

Adjacent sequences:  A264387 A264388 A264389 * A264391 A264392 A264393

KEYWORD

nonn,easy

AUTHOR

Christopher Heiling, Jan 12 2016

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)