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A048149
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Array T read by diagonals: T(i,j) = number of pairs (h,k) with h^2+k^2 <= i^2+j^2, h>=0, k >= 0.
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11
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1, 3, 3, 6, 4, 6, 11, 8, 8, 11, 17, 13, 9, 13, 17, 26, 19, 15, 15, 19, 26, 35, 28, 22, 20, 22, 28, 35, 45, 37, 30, 26, 26, 30, 37, 45, 58, 48, 39, 33, 31, 33, 39, 48, 58, 73, 62, 52, 43, 41, 41, 43, 52, 62, 73, 90, 75, 64, 54, 50, 48, 50, 54, 64, 75, 90
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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Seen as a triangle:
[0] 1;
[1] 3, 3;
[2] 6, 4, 6;
[3] 11, 8, 8, 11;
[4] 17, 13, 9, 13, 17;
[5] 26, 19, 15, 15, 19, 26;
[6] 35, 28, 22, 20, 22, 28, 35;
[7] 45, 37, 30, 26, 26, 30, 37, 45;
[8] 58, 48, 39, 33, 31, 33, 39, 48, 58;
[9] 73, 62, 52, 43, 41, 41, 43, 52, 62, 73;
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MAPLE
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A048149 := proc(n, k) option remember; ## n = 0 .. infinity and k = 0 .. n
local x, y, radius, nTotal;
if n >= k then
radius := floor(sqrt(n^2 + k^2));
nTotal := 0;
for x from 0 to radius do
nTotal := nTotal + floor(sqrt(n^2 + k^2 - x^2)) + 1;
end do;
return nTotal;
else
end if;
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MATHEMATICA
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t[i_, j_] := Module[{h, k}, Reduce[h^2 + k^2 <= i^2 + j^2 && h >= 0 && k >= 0, {h, k}, Integers] // ToRules // Length[{##}]&]; Table[t[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 26 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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