A083504 Triangle read by rows: for 1 <= k <= n, T(n, k) is the total perimeter of all squares contained in a square grid with n rows and k columns.

4, 8, 24, 12, 40, 80, 16, 56, 120, 200, 20, 72, 160, 280, 420, 24, 88, 200, 360, 560, 784, 28, 104, 240, 440, 700, 1008, 1344, 32, 120, 280, 520, 840, 1232, 1680, 2160, 36, 136, 320, 600, 980, 1456, 2016, 2640, 3300, 40, 152, 360, 680, 1120, 1680, 2352, 3120

Offset

1,1

Comments

T(n, n) = 4*A002415(n+1). Row sums are 4*A051836.

Links

Table of n, a(n) for n=1..53.

Formula

T(n, k) = (2*k^3*n + 6*k^2*n + k^2 + 4*k*n + 2*k - k^4 - 2*k^3) / 3.

Example

T(3, 2) = 40 because the six 1 X 1 squares each have perimeter 4 and the two 2 X 2 squares each have perimeter 8.

Crossrefs

Cf. A082652, A083003.

Sequence in context: A181688 A243557 A316687 * A277291 A362212 A254731

Adjacent sequences: A083501 A083502 A083503 * A083505 A083506 A083507

Keyword

nonn,tabl,easy

Author

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Jun 09 2003

Extensions

Edited by David Wasserman, Nov 18 2004

Status

approved