|
| |
|
|
A054124
|
|
Left Fibonacci row-sum array, n >= 0, 0<=k<=n.
|
|
6
|
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 4, 4, 1, 1, 1, 2, 4, 7, 5, 1, 1, 1, 2, 4, 8, 11, 6, 1, 1, 1, 2, 4, 8, 15, 16, 7, 1, 1, 1, 2, 4, 8, 16, 26, 22, 8, 1, 1, 1, 2, 4, 8, 16, 31, 42, 29, 9, 1, 1, 1, 2, 4, 8, 16, 32, 57, 64, 37, 10, 1, 1, 1, 2
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,9
|
|
|
COMMENTS
|
Reflection of array in A054123 about vertical central line.
Starting with g(0) = {0}, generate g(n) for n > 0 inductively using these rules:
(1) if x is in g(n-1), then x+1 is in g(n); and
(2) if x is in g(n-1) and x < 2, then x/2 is in g(n).
Then g(1) = {1/1}, g(2) = {1/2,2/1), g(3) = {1/4,3/2,3/1}, etc. The denominators in g(n) are 2^0, 2^1, ..., 2^(n-1), and T(n,k) is the number of occurrences of 2^k, for k = 0..n-1. - Clark Kimberling, Nov 09 2015
|
|
|
LINKS
|
Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
Index entries for triangles and arrays related to Pascal's triangle
|
|
|
FORMULA
|
T(n, 0) = T(n, n) = 1 for n >= 0; T(n, k) = T(n-1, k-1) + T(n-2, k-1) for k=1, 2, ..., n-1, n >= 2.
|
|
|
EXAMPLE
|
Rows:
1
1 1
1 1 1
1 1 2 1
1 1 2 3 1
...
|
|
|
MATHEMATICA
|
t[_, 0|1] = t[n_, n_] = 1; t[n_, k_] := t[n, k] = t[n-1, k-1] + t[n-2, k-1]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 25 2013 *)
|
|
|
PROG
|
(Haskell)
a054124 n k = a054124_tabl !! n !! k
a054124_row n = a054124_tabl !! n
a054124_tabl = map reverse a054123_tabl
-- Reinhard Zumkeller, May 26 2015
|
|
|
CROSSREFS
|
Row sums: A000045. Central numbers: 1, 1, 2, 4, 8, ... (A000079).
First n numbers of n-th column for n >= 1 form the array in A008949.
Sequence in context: A209972 A205573 A119338 * A144406 A238888 A179748
Adjacent sequences: A054121 A054122 A054123 * A054125 A054126 A054127
|
|
|
KEYWORD
|
nonn,tabl,eigen,nice
|
|
|
AUTHOR
|
Clark Kimberling
|
|
|
STATUS
|
approved
|
| |
|
|
