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A008283 Read across rows of Euler-Bernoulli or Entringer triangle. 0
1, 2, 4, 5, 10, 14, 16, 32, 46, 56, 61, 122, 178, 224, 256, 272, 544, 800, 1024, 1202, 1324, 1385, 2770, 4094, 5296, 6320, 7120, 7664, 7936, 15872, 23536, 30656, 36976, 42272, 46366, 49136, 50521, 101042, 150178, 196544, 238816, 275792, 306448, 329984, 345856 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Table of n, a(n) for n=3..47.

V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51. English version.

J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (Abstract, pdf, ps).

C. Poupard, De nouvelles significations énumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271.

EXAMPLE

This is a sub-triangle of A008282, starting in row 3 of A008282 and then proceeding as a regular triangle.

[ 3] 1

[ 4] 2, 4

[ 5] 5, 10, 14

[ 6] 16, 32, 46, 56

[ 7] 61, 122, 178, 224, 256

[ 8] 272, 544, 800, 1024, 1202, 1324

[ 9] 1385, 2770, 4094, 5296, 6320, 7120, 7664

[10] 7936, 15872, 23536, 30656, 36976, 42272, 46366, 49136

[11] 50521, 101042, 150178, 196544, 238816, 275792, 306448, 329984, 345856

MAPLE

T := proc(n, k) option remember; if k = 0 then `if`(n = 0, 1, 0) else

T(n, k - 1) + T(n - 1, n - k) fi end:

seq(seq(T(n, k-2), k = 3..n), n = 3..11); # Peter Luschny, Feb 17 2021

MATHEMATICA

T[n_, k_] := T[n, k] = If[k == 0, If[n == 0, 1, 0],

T[n, k - 1] + T[n - 1, n - k]];

Table[Table[T[n, k - 2], {k, 3, n}], {n, 3, 11}] // Flatten (* after Peter Luschny *)

CROSSREFS

Cf. A008282.

Sequence in context: A218936 A264855 A154318 * A002237 A329136 A067935

Adjacent sequences: A008280 A008281 A008282 * A008284 A008285 A008286

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 3 07:15 EST 2022. Contains 358512 sequences. (Running on oeis4.)