A303692 a(n) = n^2*(2*n - 3 - (-1)^n)/4.

0, 0, 9, 16, 50, 72, 147, 192, 324, 400, 605, 720, 1014, 1176, 1575, 1792, 2312, 2592, 3249, 3600, 4410, 4840, 5819, 6336, 7500, 8112, 9477, 10192, 11774, 12600, 14415, 15360, 17424, 18496, 20825, 22032, 24642, 25992, 28899, 30400, 33620, 35280, 38829, 40656

Offset: 1

Author

Wesley Ivan Hurt, Apr 28 2018

Keywords

• nonn
• easy

Comments

Total area of all squares with side length n such that n = s + t and s < t where s and t are positive integers.

Links

• Index entries for sequences related to partitions
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A265645.

Programs

Magma

[n^2*(2*n-3-(-1)^n)/4: n in [1..50]]; // Vincenzo Librandi, Apr 30 2018

Mathematica

Table[n^2 (2 n - 3 - (-1)^n)/4, {n, 40}]
CoefficientList[ Series[(x^5 + 7x^4 + 7x^3 + 9x^2)/((x - 1)^4 (x + 1)^3), {x, 0, 43}], x] (* or *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {0, 0, 9, 16, 50, 72, 147}, 44] (* Robert G. Wilson v, Apr 28 2018 *)

PARI

a(n) = (n-1)\2*n^2; \\ Altug Alkan, Apr 30 2018

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} n^2.

a(n) = n^2 * floor((n-1)/2).

G.f.: x^2*(x^3 + 7*x^2 + 7*x + 9)/((x - 1)^4*(x + 1)^3).

Sum_{n>=3} 1/a(n) = 9/2 - 7*Pi^2/24 - 2*log(2). - Vaclav Kotesovec, May 02 2018