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

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, 8, 7, 24, 35, 40, 39, 32, 19, 9, 8, 28, 42, 50, 52, 48, 38, 22, 10, 9, 32, 49, 60, 65, 64, 57, 44, 25, 11, 10, 36, 56, 70, 78, 80, 76, 66, 50, 28

Offset: 1

Author

Gary W. Adamson, Sep 19 2008

Keywords

• nonn
• tabl

Examples

			Partial sums by columns of the triangle (3*A144328 - 2*A000012):
  1;
  1, 1;
  1, 1, 4;
  1, 1, 4, 7;
  1, 1, 4, 7, 10;
  ...
First few rows of the triangle:
  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;
  8, 7, 24, 35, 40, 39, 32, 19;
  ...
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A000012, A064808, A144328.

Programs

Magma

A144693:= func< n,k | k eq 1 select n else (3*k-5)*(n-k+1) >;
[A144693(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Oct 19 2021

Mathematica

T[n_, k_]:= (3*k -5 +3*Boole[k==1])*(n-k+1);
Table[T[n, k], {n,12}, {k,n}]//Flatten (* G. C. Greubel, Oct 19 2021 *)

Sage

def A144693(n,k): return (3*k -5 +3*bool(k==1))*(n-k+1)
flatten([[A144693(n,k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Oct 19 2021

Formula

Sum_{k=1..n} T(n, k) = A064808(n).

T(n, k) = (3*k -5 +3*[k=1])*(n-k+1). - G. C. Greubel, Oct 19 2021