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 A173568 Triangle T(n, k) = f(k, n-k+1) + f(n-k+1, k), where f(n, k) = round( ((1+sqrt(k)^(2*n+1) - (1-sqrt(k))^(2*n+1))/(2*sqrt(k))) - 1, read by rows. 1
 6, 19, 19, 68, 56, 68, 261, 211, 211, 261, 1030, 1044, 654, 1044, 1030, 4103, 5819, 2993, 2993, 5819, 4103, 16392, 33560, 19102, 9840, 19102, 33560, 16392, 65545, 195147, 137571, 52989, 52989, 137571, 195147, 65545, 262154, 1136836, 1019606, 412700, 182270, 412700, 1019606, 1136836, 262154 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened FORMULA T(n, k) = f(k, n-k+1) + f(n-k+1, k), where f(n, k) = round( ((1+sqrt(k)^(2*n+1) - (1-sqrt(k))^(2*n+1))/(2*sqrt(k)) ) - 1. EXAMPLE Triangle begins as: 6; 19, 19; 68, 56, 68; 261, 211, 211, 261; 1030, 1044, 654, 1044, 1030; 4103, 5819, 2993, 2993, 5819, 4103; 16392, 33560, 19102, 9840, 19102, 33560, 16392; 65545, 195147, 137571, 52989, 52989, 137571, 195147, 65545; 262154, 1136836, 1019606, 412700, 182270, 412700, 1019606, 1136836, 262154; MATHEMATICA f[n_, k_]:= Round[((1+Sqrt[k])^(2*n+1) - (1-Sqrt[k])^(2*n+1))/(2*Sqrt[k])] - 1; T[n_, k_]:= f[k, n-k+1] + f[n-k+1, k]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 26 2021 *) PROG (Sage) @CachedFunction def f(n, k): return round(((1+sqrt(k))^(2*n+1) -(1-sqrt(k))^(2*n+1))/(2*sqrt(k))) -1 def T(n, k): return f(k, n-k+1) + f(n-k+1, k) flatten([[T(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 26 2021 CROSSREFS Sequence in context: A119986 A245869 A184197 * A012589 A009048 A294313 Adjacent sequences: A173565 A173566 A173567 * A173569 A173570 A173571 KEYWORD nonn,tabl,less AUTHOR Roger L. Bagula, Feb 22 2010 EXTENSIONS Edited by G. C. Greubel, Apr 26 2021 STATUS approved

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Last modified February 5 18:47 EST 2023. Contains 360087 sequences. (Running on oeis4.)