A338544 a(n) = (5*floor((n-1)/2)^2 + (4+(-1)^n)*floor((n-1)/2)) / 2.

0, 0, 0, 4, 5, 13, 15, 27, 30, 46, 50, 70, 75, 99, 105, 133, 140, 172, 180, 216, 225, 265, 275, 319, 330, 378, 390, 442, 455, 511, 525, 585, 600, 664, 680, 748, 765, 837, 855, 931, 950, 1030, 1050, 1134, 1155, 1243, 1265, 1357, 1380, 1476, 1500, 1600, 1625, 1729, 1755, 1863

Offset: 0

Author

Wesley Ivan Hurt, Nov 01 2020

Keywords

• nonn
• easy

Comments

Sum of the largest side lengths of all integer-sided triangles with perimeter 3n whose side lengths are in arithmetic progression (for example, when n=5 there are two triangles with perimeter 3*5 = 15 whose side lengths are in arithmetic progression: [3,5,7] and [4,5,6]; thus a(5) = 7+6 = 13).

Links

• Wikipedia, Integer triangle
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A028895, A050187, A147875, A211539.

Programs

Mathematica

Table[(5 Floor[(n - 1)/2]^2 + Floor[(n - 1)/2] (4 + (-1)^n))/2, {n, 0, 100}]

Formula

A147875 UNION A028895.

From Stefano Spezia, Nov 01 2020: (Start)

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

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4. (End)

16*a(n) = -14*n-1+10*n^2+(-1)^n-6*(-1)^n*n . - R. J. Mathar, Aug 19 2022