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begins:\n  0:   1;\n  1:   3;\n  2:   3,    6;\n  3:   9,   18;\n  4:   9,   36,   36;\n  5:  27,  108,  108;\n  6:  27,  162,  324,  216;\n  7:  81,  486,  972,  648;\n  8:  81,  648, 1944, 2592, 1296;\n  9: 243, 1944, 5832, 7776, 3888;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3+6*x)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 3.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3;\nP[n_, x_] := P[n, x] = Expand[(3 + 6*x)*P[n - 2, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3; for(n = 2, N, my(i = n + 1); v[i] = (3 + 6*x)*v[i - 2]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-7c641d81e21514ce","steps":[],"edges":[],"text":"A274498"},"headline":"A274498: Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=n/2).","chain":null}
