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 A174294 Triangle T(n,k), read by rows, T(n,k) = (T(n-1,k-1) + T(n-2,k-1)) - (T(n-1,k) + T(n-2,k)), with T(n, 0) = T(n, k) = 1 and T(n, 1) = (n mod 2). 6
 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, 1, 0, 0, 2, -2, 0, 1, 1, 1, 0, 0, 3, -3, 0, 1, 1, 0, 1, -2, 1, 4, -4, 0, 1, 1, 1, 0, 3, -6, 3, 5, -5, 0, 1, 1, 0, 0, 0, 6, -12, 6, 6, -6, 0, 1, 1, 1, 1, -3, 3, 9, -20, 10, 7, -7, 0, 1, 1, 0, 0, 4, -12, 12, 11, -30, 15, 8, -8, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,25 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n,k) = (T(n-1,k-1) + T(n-2,k-1)) - (T(n-1,k) + T(n-2,k)), with T(n, 0) = T(n, k) = 1 and T(n, 1) = (n mod 2). EXAMPLE Table begins: n\k|...0...1...2...3...4...5...6...7...8...9..10 ---|-------------------------------------------- 0..|...1 1..|...1...1 2..|...1...0...1 3..|...1...1...0...1 4..|...1...0...0...0...1 5..|...1...1...1..-1...0...1 6..|...1...0...0...2..-2...0...1 7..|...1...1...0...0...3..-3...0...1 8..|...1...0...1..-2...1...4..-4...0...1 9..|...1...1...0...3..-6...3...5..-5...0...1 10.|...1...0...0...0...6.-12...6...6..-6...0...1 MATHEMATICA T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==0 || k==n, 1, If[k==1, Mod[n, 2], T[n-1, k-1] +T[n-2, k-1] -T[n-1, k] -T[n-2, k] ]]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 25 2021 *) PROG (Sage) @CachedFunction def T(n, k): # A174294 if (k<0 or k>n): return 0 elif (k==0 or k==n): return 1 elif (k==1): return n%2 else: return T(n-1, k-1) + T(n-2, k-1) - T(n-1, k) - T(n-2, k) flatten([[T(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Nov 25 2021 CROSSREFS Cf. A112467, A112468, A174294, A174295, A174296, A174297. Sequence in context: A110568 A088689 A076898 * A089385 A124407 A294624 Adjacent sequences: A174291 A174292 A174293 * A174295 A174296 A174297 KEYWORD sign,tabl AUTHOR Mats Granvik, Mar 15 2010 STATUS approved

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Last modified December 3 22:01 EST 2023. Contains 367540 sequences. (Running on oeis4.)