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A308275 Sum of the perimeters of the integer-sided triangles with perimeter n whose sides lengths are square numbers. 1
0, 0, 3, 0, 0, 0, 0, 0, 9, 0, 0, 12, 0, 0, 0, 0, 0, 0, 19, 0, 0, 22, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 33, 34, 0, 36, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 48, 0, 0, 51, 0, 0, 54, 0, 0, 57, 0, 59, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 73, 0, 75, 76, 77, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..80.

Wikipedia, Integer Triangle

FORMULA

a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010052(i) * A010052(k) * A010052(n-i-k).

a(n) = n * A308064(n).

MATHEMATICA

Table[n*Sum[Sum[(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A010052, A308064.

Sequence in context: A094518 A123074 A095269 * A308254 A111417 A007271

Adjacent sequences:  A308272 A308273 A308274 * A308276 A308277 A308278

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 18 2019

STATUS

approved

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Last modified January 29 05:09 EST 2022. Contains 350672 sequences. (Running on oeis4.)