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 A100583 Number of triangles in an n X n grid of squares with diagonals. 1
 0, 8, 44, 124, 268, 492, 816, 1256, 1832, 2560, 3460, 4548, 5844, 7364, 9128, 11152, 13456, 16056, 18972, 22220, 25820, 29788, 34144, 38904, 44088, 49712, 55796, 62356, 69412, 76980, 85080, 93728, 102944, 112744, 123148, 134172, 145836 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Author?, WisFaq (Dutch) Dave Richeson, Counting triangles on a tin ceiling (solution, take 2) (2011) Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1). FORMULA a(n) = (12*n^3+18*n^2+4*n+(-1)^n-1)/4. (For a proof see the Richeson link.) a(n) = 4*Sum{i=1 to n}(i^2 + (n+1-i)*(n+1-round(i/2))). G.f.: 4*x*(x+2)*(2*x+1) / ((x-1)^4*(x+1)). - Colin Barker, Aug 19 2014 PROG (PARI) a(n)=3*n^3+9*n^2\2+n \\ Charles R Greathouse IV, Aug 19 2014 CROSSREFS Sequence in context: A290787 A188148 A316466 * A261996 A036464 A000938 Adjacent sequences: A100580 A100581 A100582 * A100584 A100585 A100586 KEYWORD nonn,easy AUTHOR Floor van Lamoen, Nov 30 2004 STATUS approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)