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%I #10 Aug 07 2021 01:13:19
%S 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,
%T 52,58,56,42,22,7,1,81,96,110,114,98,64,29,8,1,149,177,206,224,212,
%U 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
%N A Pascal type matrix based on the tribonacci numbers.
%C Row sums of A106522 mod 2 are A106524.
%H G. C. Greubel, <a href="/A106522/b106522.txt">Rows n = 0..50 of the triangle, flattened</a>
%F Riordan array (1/(1-x-x^2-x^3), x/(1-x)).
%F Number triangle T(n, 0) = A000073(n+2), T(n, k) = T(n-1, k-1) + T(n-1, k).
%F Sum_{k=0..n} T(n,k) = A001590(n+3).
%F Sum_{k=0..floor(n/2)} T(n-k, k) = A106523(n).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 2, 1;
%e 4, 4, 3, 1;
%e 7, 8, 7, 4, 1;
%e 13, 13, 15, 11, 5, 1;
%t b[n_]:= b[n]= If[n<2, 0, If[n==2, 1, b[n-1] +b[n-2] +b[n-3]]]; (* A000073 *)
%t 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]]];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Aug 06 2021 *)
%o (Sage)
%o @CachedFunction
%o def b(n): return 0 if (n<2) else 1 if (n==2) else b(n-1) +b(n-2) +b(n-3)
%o def T(n,k):
%o if (k<0 or k>n): return 0
%o elif (k==0): return b(n+2)
%o else: return T(n-1, k) + T(n-1, k-1)
%o flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Aug 06 2021
%Y Cf. A000073, A001590 (row sums), A106523 (diagonal sums).
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, May 06 2005
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