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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 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

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