cp's OEIS Frontend

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

%I A008283 #31 Jul 08 2025 01:02:27
%S A008283 1,2,4,5,10,14,16,32,46,56,61,122,178,224,256,272,544,800,1024,1202,
%T A008283 1324,1385,2770,4094,5296,6320,7120,7664,7936,15872,23536,30656,36976,
%U A008283 42272,46366,49136,50521,101042,150178,196544,238816,275792,306448,329984,345856
%N A008283 Read across rows of Euler-Bernoulli or Entringer triangle.
%H A008283 V. I. Arnold, <a href="http://mi.mathnet.ru/eng/umn4470">The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups</a>, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51. <a href="http://iopscience.iop.org/article/10.1070/RM1992v047n01ABEH000861/pdf">English version</a>.
%H A008283 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 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H A008283 C. Poupard, <a href="http://dx.doi.org/10.1016/0012-365X(82)90293-X">De nouvelles significations énumeratives des nombres d'Entringer</a>, Discrete Math., 38 (1982), 265-271.
%e A008283 This is a sub-triangle of A008282, starting in row 3 of A008282 and then proceeding as a regular triangle.
%e A008283 [ 3] 1
%e A008283 [ 4] 2,     4
%e A008283 [ 5] 5,     10,     14
%e A008283 [ 6] 16,    32,     46,     56
%e A008283 [ 7] 61,    122,    178,    224,    256
%e A008283 [ 8] 272,   544,    800,    1024,   1202,   1324
%e A008283 [ 9] 1385,  2770,   4094,   5296,   6320,   7120,   7664
%e A008283 [10] 7936,  15872,  23536,  30656,  36976,  42272,  46366,  49136
%e A008283 [11] 50521, 101042, 150178, 196544, 238816, 275792, 306448, 329984, 345856
%p A008283 T := proc(n, k) option remember; if k = 0 then `if`(n = 0, 1, 0) else
%p A008283 T(n, k - 1) + T(n - 1, n - k) fi end:
%p A008283 seq(seq(T(n, k-2), k = 3..n), n = 3..11); # _Peter Luschny_, Feb 17 2021
%t A008283 T[n_, k_] := T[n, k] = If[k == 0, If[n == 0, 1, 0],
%t A008283      T[n, k - 1] + T[n - 1, n - k]];
%t A008283 Table[Table[T[n, k - 2], {k, 3, n}], {n, 3, 11}] // Flatten (* after _Peter Luschny_ *)
%Y A008283 Cf. A008282.
%K A008283 nonn,tabl
%O A008283 3,2
%A A008283 _N. J. A. Sloane_