-1003

Appears in sequences

• a(0) = -1 and a(n) = (-1)^(n+1)*(3*n^2 - n + 4)/2 for n >= 1.at n=26A173247
• Array of coefficients of powers of x^2 for S(2*n,x)^3 with Chebyshev's S polynomials A049310.at n=31A220666
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 129", based on the 5-celled von Neumann neighborhood.at n=19A270220
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 411", based on the 5-celled von Neumann neighborhood.at n=21A271892
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 465", based on the 5-celled von Neumann neighborhood.at n=23A272317
• Expansion of 1 - x/(1 - x^3/(1 - x^6/(1 - x^10/(1 - x^15/(1 - x^21/(1 - ... - x^(n*(n+1)/2)/(1 - ...))))))), a continued fraction.at n=49A290976
• Martingale win/loss triangle, read by rows: T(n,k) = total number of dollars won (or lost) using the martingale method on all possible n trials that have exactly k losses and n-k wins, for 0 <= k <= n.at n=64A355659
• G.f. A(x) satisfies A(x) = 1 + x*A(x)/A(-x*A(x)^3)^2.at n=7A384974
• Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A384974.at n=43A384977