-1471

Appears in sequences

• Let a_0 = 1 and for n > 0, let a_n be the smallest positive integer not already in the sequence such that (a_0 + a_1 x + a-2x^2 + ....)^(1/3) has integer coefficients. (Hanna's A083349). Let f(n) = n th term in the present sequence. Then a_0 + a_1 x + a_2 x^2 + ... = (1-x)^f(1) (1-x^2)^f(2) (1-x^3)^f(3) ....at n=27A110879
• Triangle T that satisfies the matrix products: C*[T^-1]*C = T and T*[C^-1]*T = C, where C is Pascal's triangle.at n=50A118801
• a(n) = A174817(n) - Mnr; where Mnr = A001228(26) = 808017424794512875886459904961710757005754368000000000, also called the Monster number, cf. A003131.at n=24A174818
• A symmetrical triangle of leading ones adjusted polynomial coefficients based on Hermite orthogonal polynomials: t(n,m)=CoefficientList[HermiteH[n, x], x][[m + 1]] + Reverse[CoefficientList[ HermiteH[n, x], x]][[m + 1]] - (CoefficientList[HermiteH[n, x], x][[1]] + Reverse[CoefficientList[HermiteH[n, x], x]][[1]]) + 1.at n=30A176411
• A symmetrical triangle of leading ones adjusted polynomial coefficients based on Hermite orthogonal polynomials: t(n,m)=CoefficientList[HermiteH[n, x], x][[m + 1]] + Reverse[CoefficientList[ HermiteH[n, x], x]][[m + 1]] - (CoefficientList[HermiteH[n, x], x][[1]] + Reverse[CoefficientList[HermiteH[n, x], x]][[1]]) + 1.at n=33A176411
• Prime-generating polynomial: a(n) = 4*n^2 + 12*n - 1583.at n=4A182409
• Values of the prime-generating polynomial 4*n^2 - 284*n + 3449.at n=30A210626
• Values of the prime-generating polynomial 4*n^2 - 284*n + 3449.at n=41A210626
• Irregular triangle read by rows: coefficients of polynomials V_n(x), highest degree terms first.at n=60A257597
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 278", based on the 5-celled von Neumann neighborhood.at n=43A271098
• First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 297", based on the 5-celled von Neumann neighborhood.at n=21A271151
• a(n) = [x^n] Product_{k>=1} ((1 + x^(2*k-1))/(1 + x^(2*k)))^n.at n=12A296043
• G.f. satisfies A(x) = 1 + x * A(x * (1 - x)).at n=11A360894