A140303 Triangle T(n,k) = 3^(n-k) read by rows.

1, 3, 1, 9, 3, 1, 27, 9, 3, 1, 81, 27, 9, 3, 1, 243, 81, 27, 9, 3, 1, 729, 243, 81, 27, 9, 3, 1, 2187, 729, 243, 81, 27, 9, 3, 1, 6561, 2187, 729, 243, 81, 27, 9, 3, 1, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3, 1, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3, 1

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, May 27 2008

Keywords

• nonn
• tabl

Comments

Row sums are: 1, 4, 13, 40, 121, 364, .. A003462(n+1).

Examples

			1;
3, 1;
9, 3, 1;
27, 9, 3, 1;
81, 27, 9, 3, 1;
243, 81, 27, 9, 3, 1;
729, 243, 81, 27, 9, 3, 1;
2187, 729, 243, 81, 27, 9, 3, 1;
6561, 2187, 729, 243, 81, 27, 9, 3, 1;
19683, 6561, 2187, 729, 243, 81, 27, 9, 3, 1;
59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3, 1;
		

References

• Advanced Number Theory, Harvey Cohn, Dover Books, 1963, Page 232

Crossrefs

Cf. A130321.

Programs

Mathematica

Clear[p, a] a = 3; p[x, 0] = 1; p[x_, n_] := p[x, n] = Sum[a^i*x^(n - i), {i, 0, n}]; Table[p[x, n], {n, 0, 10}]; a0 = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a0] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]
Table[3^(n-k),{n,15},{k,n}]//Flatten (* Harvey P. Dale, Nov 14 2021 *)

Formula

T(n,k) = A000244(n-k) . - R. J. Mathar, Sep 12 2013