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

1,2

Links

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

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

Example

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;
  ...

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 *)

Prog

(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
(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

Crossrefs

Cf. A000012, A064808, A144328.

Sequence in context: A034390 A368671 A183912 * A328399 A328171 A029139

Adjacent sequences: A144690 A144691 A144692 * A144694 A144695 A144696

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 19 2008

Status

approved