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A108040 Reflection of triangle in A008280 in vertical axis. 5
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, 0, 272, 544, 800, 1024, 1202, 1324, 1385, 1385, 7936, 7936, 7664, 7120, 6320, 5296, 4094, 2770, 1385, 0, 0, 7936, 15872, 23536, 30656 (list; table; graph; refs; listen; history; text; internal format)
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

Index entries for sequences related to 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

CROSSREFS

See A008280 and A008281 for other versions, additional references, formulas, etc.

Sequence in context: A133418 A181169 A029390 * A137566 A258277 A122865

Adjacent sequences:  A108037 A108038 A108039 * A108041 A108042 A108043

KEYWORD

nonn,tabl,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. J. Mathar, May 02 2007

STATUS

approved

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Last modified July 19 08:12 EDT 2019. Contains 325155 sequences. (Running on oeis4.)