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begins:\n  0:  1;\n  1:  2;\n  2:  2,   2;\n  3:  4,   4;\n  4:  4,   8,   4;\n  5:  8,  16,   8;\n  6:  8,  24,  24,   8;\n  7: 16,  48,  48,  16;\n  8: 16,  64,  96,  64, 16;\n  9: 32, 128, 192, 128, 32;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2+2*x)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2;\nP[n_, x_] := P[n, x] = Expand[(2 + 2*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] = 2; for(n = 2, N, my(i = n + 1); v[i] = (2 + 2*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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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}},{"oeis_id":"A274496","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:  1;\n  1:  2;\n  2:  2,   2;\n  3:  4,   4;\n  4:  4,   8,   4;\n  5:  8,  16,   8;\n  6:  8,  24,  24,   8;\n  7: 16,  48,  48,  16;\n  8: 16,  64,  96,  64, 16;\n  9: 32, 128, 192, 128, 32;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (2+2*x)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2;\nP[n_, x_] := P[n, x] = Expand[(2 + 2*x)*P[n - 2, x]];\nTable[Reverse[CoefficientList[P[n, x], x]], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2; for(n = 2, N, my(i = n + 1); v[i] = (2 + 2*x)*v[i - 2]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = Vecrev(c); 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":true,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-b6aca576a689e9f0","steps":[],"edges":[],"text":"A274496"},"headline":"A274496: Triangle read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2).","chain":null}