A308123 Sum of the perimeters of all integer-sided isosceles triangles with perimeter n.

0, 0, 3, 0, 5, 6, 14, 8, 18, 20, 33, 24, 39, 42, 60, 48, 68, 72, 95, 80, 105, 110, 138, 120, 150, 156, 189, 168, 203, 210, 248, 224, 264, 272, 315, 288, 333, 342, 390, 360, 410, 420, 473, 440, 495, 506, 564, 528, 588, 600, 663, 624, 689, 702, 770, 728, 798

Offset

1,3

Links

Table of n, a(n) for n=1..57.

Wikipedia, Integer Triangle

Index entries for linear recurrences with constant coefficients, signature (1,0,0,2,-2,0,0,-1,1).

Formula

a(n) = n * A059169(n).

a(n) = n*(2*n-3-2*cos(n*Pi/2)-3*cos(n*Pi)-2*sin(n*Pi/2))/8.

From Colin Barker, May 14 2019: (Start)

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

a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9) for n>9.

(End)

E.g.f.: x*((1 + x)*cosh(x) - cos(x) + (x - 2)*sinh(x) + sin(x))/4. - Stefano Spezia, Nov 04 2021

Mathematica

Table[n*(2*n - 3 - 2*Cos[n*Pi/2] - 3*Cos[n*Pi] - 2*Sin[n*Pi/2])/8, {n, 100}]

Crossrefs

Cf. A059169.

Sequence in context: A052483 A373775 A308116 * A308089 A249859 A213724

Adjacent sequences: A308120 A308121 A308122 * A308124 A308125 A308126

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 13 2019

Status

approved