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A308303 Number of integer-sided triangles with perimeter n and at least one even side length. 0
0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 6, 8, 9, 10, 9, 12, 12, 14, 12, 16, 16, 19, 16, 21, 20, 24, 20, 27, 25, 30, 25, 33, 30, 37, 30, 40, 36, 44, 36, 48, 42, 52, 42, 56, 49, 61, 49, 65, 56, 70, 56, 75, 64, 80, 64, 85, 72, 91, 72, 96, 81, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

LINKS

Table of n, a(n) for n=1..70.

Wikipedia, Integer Triangle

FORMULA

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

a(n) = A005044(n) - A308065(n).

MATHEMATICA

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

CROSSREFS

Cf. A005044, A308065.

Sequence in context: A265409 A126257 A025773 * A285763 A294621 A029077

Adjacent sequences:  A308300 A308301 A308302 * A308304 A308305 A308306

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 19 2019

STATUS

approved

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Last modified July 12 06:20 EDT 2020. Contains 335658 sequences. (Running on oeis4.)