A347584 Triangle formed by Pascal's rule, except that the n-th row begins and ends with the n-th Lucas number.
2, 1, 1, 3, 2, 3, 4, 5, 5, 4, 7, 9, 10, 9, 7, 11, 16, 19, 19, 16, 11, 18, 27, 35, 38, 35, 27, 18, 29, 45, 62, 73, 73, 62, 45, 29, 47, 74, 107, 135, 146, 135, 107, 74, 47, 76, 121, 181, 242, 281, 281, 242, 181, 121, 76, 123, 197, 302, 423, 523, 562, 523, 423, 302, 197, 123
Offset: 0
Keywords
Examples
The first two Lucas numbers (for n=0 and n=1) are 2 and 1, so the first two rows (again, for n=0 and n=1) of the triangle are 2 and 1, 1 respectively.
Triangle begins:
2;
1, 1;
3, 2, 3;
4, 5, 5, 4;
7, 9, 10, 9, 7;
11, 16, 19, 19, 16, 11;
18, 27, 35, 38, 35, 27, 18;
Crossrefs
Programs
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Mathematica
T[n_, 0] := LucasL[n]; T[n_, n_] := LucasL[n]; T[n_, k_] := T[n - 1, k - 1] + T[n - 1, k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
Comments