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 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. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS T(n, n) = 4*A002415(n+1). Row sums are 4*A051836. LINKS FORMULA T(n, k) = (2k^3*n+6k^2*n+k^2+4k*n+2k-k^4-2k^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 A254731 A291548 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

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Last modified June 26 19:25 EDT 2022. Contains 354885 sequences. (Running on oeis4.)