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A227862 A boustrophedon triangle. 4
1, 1, 2, 4, 3, 1, 1, 5, 8, 9, 24, 23, 18, 10, 1, 1, 25, 48, 66, 76, 77, 294, 293, 268, 220, 154, 78, 1, 1, 295, 588, 856, 1076, 1230, 1308, 1309, 6664, 6663, 6368, 5780, 4924, 3848, 2618, 1310, 1, 1, 6665, 13328, 19696, 25476, 30400, 34248, 36866, 38176, 38177 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

T(n, n * (n mod 2)) = A000667(n).

LINKS

Reinhard Zumkeller, Rows n = 0..125 of table, flattened

Peter Luschny, An old operation on sequences: the Seidel transform.

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]

Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT]

Wikipedia, Boustrophedon transform.

Index entries for sequences related to boustrophedon transform

EXAMPLE

First nine rows:

.  0:                                    1

.  1:                               1   ->  2

.  2:                           4   <-   3  <-  1

.  3:                       1 ->    5 ->   8   ->   9

.  4:                   24  <-  23  <-  18  <-  10  <-  1

.  5:              1  ->  25  ->  48  ->   66 ->   76  ->  77

.  6:          294 <-  293 <-  268 <-  220 <-  154  <-  78   <-  1

.  7:      1  ->  295 ->  588 ->  856 -> 1076 -> 1230 -> 1308 -> 1309

.  8:  6664 <- 6663 <- 6368 <- 5780 <- 4924 <- 3848 <- 2618 <- 1310  <- 1 .

MATHEMATICA

T[0, 0] = 1; T[n_?OddQ, 0] = 1; T[n_?EvenQ, n_] = 1; T[n_, k_] /; 0 <= k <= n := T[n, k] = If[OddQ[n], T[n, k - 1] + T[n - 1, k - 1], T[n, k + 1] + T[n - 1, k]]; T[_, _] = 0;

Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 23 2019 *)

PROG

(Haskell)

a227862 n k = a227862_tabl !! n !! k

a227862_row n = a227862_tabl !! n

a227862_tabl = map snd $ iterate ox (False, [1]) where

   ox (turn, xs) = (not turn, if turn then reverse ys else ys)

      where ys = scanl (+) 1 (if turn then reverse xs else xs)

CROSSREFS

Cf. A008280.

Sequence in context: A085008 A285587 A134893 * A229802 A106581 A317612

Adjacent sequences:  A227859 A227860 A227861 * A227863 A227864 A227865

KEYWORD

nonn,tabl,look

AUTHOR

Reinhard Zumkeller, Nov 01 2013

STATUS

approved

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Last modified September 20 10:24 EDT 2020. Contains 337264 sequences. (Running on oeis4.)