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 A208532 Mirror image of triangle in A125185; unsigned version of A120058. 2
 1, 2, 1, 3, 4, 2, 4, 9, 10, 4, 5, 16, 28, 24, 8, 6, 25, 60, 80, 56, 16, 7, 36, 110, 200, 216, 128, 32, 8, 49, 182, 420, 616, 560, 288, 64, 9, 64, 280, 784, 1456, 1792, 1408, 640, 128, 10, 81, 408, 1344, 3024, 4704, 4992, 3456, 1408, 256 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Subtriangle of the triangle given by (1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Equals A007318*A134309*A097806 as infinite lower triangular matrix. Row sums are powers of 3 (A000244). Diagonal sums are powers of 2 (A000079). LINKS FORMULA T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-1,k-1), T(0,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. G.f.: (1-y*x)/((1-x)*(1-(1+2*y)*x)). Sum_{k, 0<=k<=n} T(n,k)*x^k = A083085(n), A084567(n), A000012(n), A000027(n+1), A000244(n), A083065(n), A083076(n) for x = -3, -2, -1, 0, 1, 2, 3 respectively. EXAMPLE Triangle begins : 1 2, 1 3, 4, 2 4, 9, 10, 4 5, 16, 28, 24, 8 6, 25, 60, 80, 56, 16 7, 36, 110, 200, 216, 128, 32 8, 49, 182, 420, 616, 560, 288, 64 9, 64, 280, 784, 1456, 1792, 1408, 640, 128 10, 81, 408, 1344, 3024, 4704, 4992, 3456, 1408, 256 Triangle (1, 1, -1, 1, 0, 0, 0, ...) DELTA (0, 1, 1, 0, 0, 0, ...) begins : 1 1, 0 2, 1, 0 3, 4, 2, 0 4, 9, 10, 4, 0 5, 16, 28, 24, 8, 0 6, 25, 60, 80, 56, 16, 0 CROSSREFS Cf. Columns: A000027, A000290, A006331, A112742. Cf. Diagonals: A011782, 2*A045623, Sequence in context: A125100 A128544 A120058 * A245334 A102756 A086614 Adjacent sequences:  A208529 A208530 A208531 * A208533 A208534 A208535 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 27 2012 STATUS approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)