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

0,2

Comments

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

References

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

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

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;

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 *)

Crossrefs

Cf. A130321.

Sequence in context: A021762 A019736 A213595 * A249266 A309057 A246269

Adjacent sequences: A140300 A140301 A140302 * A140304 A140305 A140306

Keyword

nonn,tabl

Author

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

Status

approved