The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307966 Sum of the largest side lengths of all integer-sided triangles with perimeter n. 2
 0, 0, 1, 0, 2, 2, 6, 3, 11, 8, 19, 14, 28, 23, 45, 33, 59, 52, 83, 67, 109, 93, 141, 121, 175, 155, 224, 191, 267, 243, 327, 288, 390, 351, 462, 417, 537, 492, 634, 570, 722, 671, 834, 762, 950, 878, 1078, 998, 1210, 1130, 1371, 1266, 1520, 1432, 1700, 1585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Table of n, a(n) for n=1..56. FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * (n-i-k). Conjectures from Colin Barker, May 12 2019: (Start) G.f.: x^3*(1 + x + 2*x^2 + 2*x^3 + 4*x^4 + 3*x^5 + 3*x^6) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2). a(n) = -a(n-1) + 2*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) - 5*a(n-7) - 5*a(n-8) - a(n-9) + 2*a(n-10) + 4*a(n-11) + 2*a(n-12) - a(n-14) - a(n-15) for n>15. (End) MATHEMATICA Table[Sum[Sum[(n - i - k)*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}] PROG (PARI) a(n) = sum(k=1, n\3, sum(i=k, (n-k)\2, sign((i+k)\(n-i-k+1)) * (n-i-k))); \\ Michel Marcus, May 13 2019 CROSSREFS Cf. A005044. Sequence in context: A240578 A273105 A370370 * A129889 A263673 A304987 Adjacent sequences: A307963 A307964 A307965 * A307967 A307968 A307969 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 11 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 22:34 EDT 2024. Contains 375058 sequences. (Running on oeis4.)