A008283 Read across rows of Euler-Bernoulli or Entringer triangle.

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

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