A106522 A Pascal type matrix based on the tribonacci numbers.
1, 1, 1, 2, 2, 1, 4, 4, 3, 1, 7, 8, 7, 4, 1, 13, 15, 15, 11, 5, 1, 24, 28, 30, 26, 16, 6, 1, 44, 52, 58, 56, 42, 22, 7, 1, 81, 96, 110, 114, 98, 64, 29, 8, 1, 149, 177, 206, 224, 212, 162, 93, 37, 9, 1, 274, 326, 383, 430, 436, 374, 255, 130, 46, 10, 1, 504, 600, 709, 813, 866, 810, 629, 385, 176, 56, 11, 1
Offset: 0
Examples
Triangle begins: 1; 1, 1; 2, 2, 1; 4, 4, 3, 1; 7, 8, 7, 4, 1; 13, 13, 15, 11, 5, 1;
Links
- G. C. Greubel, Rows n = 0..50 of the triangle, flattened
Programs
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Mathematica
b[n_]:= b[n]= If[n<2, 0, If[n==2, 1, b[n-1] +b[n-2] +b[n-3]]]; (* A000073 *) T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==0, b[n+2], T[n-1, k-1] +T[n-1, k]]]; Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Aug 06 2021 *)
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Sage
@CachedFunction def b(n): return 0 if (n<2) else 1 if (n==2) else b(n-1) +b(n-2) +b(n-3) def T(n,k): if (k<0 or k>n): return 0 elif (k==0): return b(n+2) else: return T(n-1, k) + T(n-1, k-1) flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Aug 06 2021
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