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

Author

N. J. A. Sloane

Keywords

• nonn
• tabl

Examples

			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
		

Links

• 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.

Crossrefs

Cf. A008282.

Programs

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 *)