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A308158 Sum of the smallest sides of all integer-sided isosceles triangles with perimeter n. 2
0, 0, 1, 0, 1, 2, 3, 2, 4, 5, 7, 6, 8, 10, 13, 11, 14, 17, 20, 18, 22, 25, 29, 27, 31, 35, 40, 37, 42, 47, 52, 49, 55, 60, 66, 63, 69, 75, 82, 78, 85, 92, 99, 95, 103, 110, 118, 114, 122, 130, 139, 134, 143, 152, 161, 156, 166, 175, 185, 180, 190, 200, 211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..63.

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))) * ([i=k] + [i=n-i-k] - [k=n-i-k]) * k, where [] is the Iverson bracket.

Conjectures from Colin Barker, May 15 2019: (Start)

G.f.: x^3*(1 + x^2 + x^3 + x^4 + x^5) / ((1 - x)^3*(1 + x)^2*(1 + x^2)^2*(1 + x + x^2)).

a(n) = a(n-3) + 2*a(n-4) - 2*a(n-7) - a(n-8) + a(n-11) for n>11.

(End)

MATHEMATICA

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

CROSSREFS

Cf. A059169.

Sequence in context: A322791 A304745 A176789 * A325349 A320054 A215228

Adjacent sequences:  A308155 A308156 A308157 * A308159 A308160 A308161

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 14 2019

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)