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begins:\n  0: 1;\n  1: 1;\n  2: 1,  2;\n  3: 1,  4;\n  4: 1,  6,  4;\n  5: 1,  8, 12;\n  6: 1, 10, 24,   8;\n  7: 1, 12, 40,  32;\n  8: 1, 14, 60,  80, 16;\n  9: 1, 16, 84, 160, 80;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = P(n-1,x) + 2*x*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[P[n - 1, x] + 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] = 1; for(n = 2, N, my(i = n + 1); v[i] = v[i - 1] + 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, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A128099","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0: 1;\n  1: 1;\n  2: 1,  2;\n  3: 1,  4;\n  4: 1,  6,  4;\n  5: 1,  8, 12;\n  6: 1, 10, 24,   8;\n  7: 1, 12, 40,  32;\n  8: 1, 14, 60,  80, 16;\n  9: 1, 16, 84, 160, 80;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = P(n-1,x) + 2*x*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[P[n - 1, x] + 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] = 1; for(n = 2, N, my(i = n + 1); v[i] = v[i - 1] + 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, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-e3d901814302c059","steps":[],"edges":[],"text":"A128099"},"headline":"A128099: Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles (0 <= k <= floor(n/2)).","chain":null}