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A193970 Mirror of the triangle A193969. 2
1, 3, 1, 7, 4, 1, 21, 12, 7, 2, 54, 33, 19, 11, 3, 144, 88, 54, 31, 18, 5, 376, 232, 142, 87, 50, 29, 8, 987, 609, 376, 230, 141, 81, 47, 13, 2583, 1596, 985, 608, 372, 228, 131, 76, 21, 6765, 4180, 2583, 1594, 984, 602, 369, 212, 123, 34, 17710, 10945, 6763 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A193969 is obtained by reversing the rows of the triangle A193970.
LINKS
FORMULA
Write w(n,k) for the triangle at A193969. The triangle at A193970 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
3....1
7....4....1
21...12...7....2
54...33...19...11...3
144..88...54...31...18...5
MATHEMATICA
z = 12;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
q[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, n}];
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193969 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193970 *)
CROSSREFS
Cf. A193969.
Sequence in context: A210038 A319076 A286513 * A274510 A158841 A213576
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)