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A144693 Triangle read by rows, A000012 * (3*A144328 - 2*A000012), where A000012 means a lower triangular matrix of all 1's.

%I A144693 #14 Sep 08 2022 08:45:38
%S A144693 1,2,1,3,2,4,4,3,8,7,5,4,12,14,10,6,5,16,21,20,13,7,6,20,28,30,26,16,
%T A144693 8,7,24,35,40,39,32,19,9,8,28,42,50,52,48,38,22,10,9,32,49,60,65,64,
%U A144693 57,44,25,11,10,36,56,70,78,80,76,66,50,28
%N A144693 Triangle read by rows, A000012 * (3*A144328 - 2*A000012), where A000012 means a lower triangular matrix of all 1's.
%H A144693 G. C. Greubel, <a href="/A144693/b144693.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A144693 Sum_{k=1..n} T(n, k) = A064808(n).
%F A144693 T(n, k) = (3*k -5 +3*[k=1])*(n-k+1). - _G. C. Greubel_, Oct 19 2021
%e A144693 Partial sums by columns of the triangle (3*A144328 - 2*A000012):
%e A144693   1;
%e A144693   1, 1;
%e A144693   1, 1, 4;
%e A144693   1, 1, 4, 7;
%e A144693   1, 1, 4, 7, 10;
%e A144693   ...
%e A144693 First few rows of the triangle:
%e A144693   1;
%e A144693   2, 1
%e A144693   3, 2,  4;
%e A144693   4, 3,  8,  7;
%e A144693   5, 4, 12, 14, 10;
%e A144693   6, 5, 16, 21, 20, 13;
%e A144693   7, 6, 20, 28, 30, 26, 16;
%e A144693   8, 7, 24, 35, 40, 39, 32, 19;
%e A144693   ...
%t A144693 T[n_, k_]:= (3*k -5 +3*Boole[k==1])*(n-k+1);
%t A144693 Table[T[n, k], {n,12}, {k,n}]//Flatten (* _G. C. Greubel_, Oct 19 2021 *)
%o A144693 (Magma)
%o A144693 A144693:= func< n,k | k eq 1 select n else (3*k-5)*(n-k+1) >;
%o A144693 [A144693(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Oct 19 2021
%o A144693 (Sage)
%o A144693 def A144693(n,k): return (3*k -5 +3*bool(k==1))*(n-k+1)
%o A144693 flatten([[A144693(n,k) for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Oct 19 2021
%Y A144693 Cf. A000012, A064808, A144328.
%K A144693 nonn,tabl
%O A144693 1,2
%A A144693 _Gary W. Adamson_, Sep 19 2008