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A058294
Successive rows of a triangle, the columns of which are generalized Fibonacci sequences S(j).
10
1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 7, 10, 7, 3, 1, 1, 4, 13, 30, 43, 30, 13, 4, 1, 1, 5, 21, 68, 157, 225, 157, 68, 21, 5, 1, 1, 6, 31, 130, 421, 972, 1393, 972, 421, 130, 31, 6, 1, 1, 7, 43, 222, 931, 3015, 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1
OFFSET
1,6
COMMENTS
From Reinhard Zumkeller, Sep 14 2014: (Start)
T(n,k) = A102473(n,k), k=1..n;
T(n,k) = A102472(n,k-n+1), k=n..2*n-1;
T(n,n) = A001040(n). (End)
FORMULA
The j-th column S(j) is generated by a(n+1) = (n+j)*a(n) + a(n-1), a(0)=0, a(1)=1.
EXAMPLE
Triangle begins:
1;
1, 1, 1;
1, 2, 3, 2, 1;
1, 3, 7, 10, 7, 3, 1;
...
MATHEMATICA
t[n_, n_] = 1; t[n_, k_] := t[n, k] = If[n<k, 0, (n-1)*t[n-1, k] + t[n-2, k]]; row[n_] := With[{ro = Table[t[n, k], {k, 1, n}]}, Join[Reverse[ro], Rest[ro]]]; Array[row, 8] // Flatten (* Jean-François Alcover, Oct 05 2016 *)
PROG
(Haskell)
a058294 n k = a058294_tabf !! (n-1) !! (k-1)
a058294_row n = a058294_tabf !! (n-1)
a058294_tabf = [1] : zipWith (++) xss (map (tail . reverse) xss)
where xss = tail a102473_tabl
-- Reinhard Zumkeller, Sep 14 2014
CROSSREFS
A001040, A001053, A058307, A058308, A058309 are columns of this triangle.
Sequence in context: A026323 A017838 A181567 * A323834 A082868 A219539
KEYWORD
nonn,tabf,nice,easy
AUTHOR
Russell Walsmith, Dec 07 2000
STATUS
approved