OFFSET
0,7
LINKS
Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened
Dominique Foata, Guo-Niu Han, André Permutation Calculus; a Twin Seidel Matrix Sequence, arXiv:1601.04371 [math.CO], 2016.
Peter Luschny, An old operation on sequences: the Seidel transform
G. Viennot, Interprétations combinatoires des nombres d'Euler et de Genocchi, Séminaire de théorie des nombres, 1980/1981, Exp.No. 11, p. 41, Univ. Bordeaux I, Talence, 1982.
Wikipedia, Boustrophedon transform
FORMULA
a(n,k) = A008280(n,n-k). - R. J. Mathar, May 02 2007
EXAMPLE
This version of the triangle begins:
.............1
...........1...0
.........0...1...1
.......2...2...1...0
.....0...2...4...5...5
..16..16..14..10...5...0
Kempner tableau begins:
....................1
....................1....0
...............0....1....1
...............2....2....1....0
..........0....2....4....5....5
.........16...16...14...10....5...0
.....0...16...32...46...56...61..61
...272..272..256..224..178..122..61..0
Column 1,1,1,2,4,14,46,224, ... is A005437.
Column 1,1,5,10,56,178, ... is A005438.
MAPLE
A008281 := proc(h, k) option remember ; if h=1 and k=1 or h=0 then RETURN(1) ; elif h>=1 and k> h then RETURN(0) ; elif h=k then RETURN( A008281(h, h-1)) ; else RETURN( add(A008281(h-1, j), j=h-k..h-1) ) ; fi ; end: A008280 := proc(h, k) if ( h <= 1 ) or ( h mod 2) = 1 then A008281(h, k) ; else A008281(h, h-k) ; fi ; end: A108040 := proc(h, k) A008280(h, h-k) ; end: for h from 0 to 13 do for k from 0 to h do printf("%d, ", A108040(h, k)) ; od ; od ; # R. J. Mathar, May 02 2007
MATHEMATICA
max = 11; t[0, 0] = 1; t[n_, m_] /; n<m || m<0 = 0; t[n_, m_] := t[n, m] = Sum[t[n-1, n-k], {k, m}]; tri = Table[t[n, m], {n, 0, max}, {m, 0, n}]; A008280 = {Reverse[#[[1]]], #[[2]]}& /@ Partition[tri, 2] // Flatten[#, 1]&; A108040 = Reverse /@ A008280; A108040 // Flatten (* Jean-François Alcover, Jan 08 2014 *)
PROG
(Haskell)
a108040 n k = a108040_tabl !! n !! k
a108040_row n = a108040_tabl !! k
a108040_tabl = ox False a008281_tabl where
ox turn (xs:xss) = (if turn then reverse xs else xs) : ox (not turn) xss
-- Reinhard Zumkeller, Nov 01 2013
(Python) # Uses function seidel from A008281.
def A108040row(n): return seidel(n)[::-1] if n % 2 else seidel(n)
for n in range(8): print(A108040row(n)) # Peter Luschny, Jun 01 2022
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, May 02 2007
STATUS
approved