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A140303 Triangle T(n,k) = 3^(n-k) read by rows. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved

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Last modified March 1 22:22 EST 2024. Contains 370443 sequences. (Running on oeis4.)