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A308253 Number of integer-sided triangles with perimeter n and nonprime side lengths. 3
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 3, 4, 2, 4, 4, 5, 3, 5, 4, 7, 6, 7, 8, 10, 6, 9, 8, 11, 7, 10, 8, 13, 11, 14, 15, 18, 11, 16, 14, 19, 19, 21, 20, 26, 26, 28, 30, 33, 25, 30, 30, 34, 27, 32, 29, 37, 35, 39, 40, 45, 44, 47, 47, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,18

LINKS

Table of n, a(n) for n=1..74.

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))) * c(i) * c(k) * c(n-i-k), where c(n) = A005171(n).

MATHEMATICA

Table[Sum[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[n - i - k - 1]) Sign[

Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A005171.

Sequence in context: A052275 A338139 A244798 * A286614 A023508 A151553

Adjacent sequences:  A308250 A308251 A308252 * A308254 A308255 A308256

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 17 2019

STATUS

approved

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)