A062704 Di-Boustrophedon transform of all 1's sequence: Fill in an array by diagonals alternating in the 'up' and 'down' directions. Each diagonal starts with a 1. When going in the 'up' direction the next element is the sum of the previous element of the diagonal and the previous two elements of the row the new element is in. When going in the 'down' direction the next element is the sum of the previous element of the diagonal and the previous two elements of the column the new element is in. The final element of the n-th diagonal is a(n).

1, 2, 5, 13, 40, 145, 616, 3017, 16752, 103973, 713040, 5352729, 43645848, 384059537, 3626960272, 36585357429, 392545057280, 4463791225145, 53622168102640, 678508544425721, 9020035443775264, 125684948107190045, 1831698736650660952, 27866044704218390113

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Example

The array begins:
   1   2   1  13   1
   1   3  10  14
   5   6  25
   1  34
  40

Maple

T:= proc(n, k) option remember;
      if n<1 or k<1 then 0
    elif n=1 and irem(k, 2)=1 or k=1 and irem(n, 2)=0 then 1
    elif irem(n+k, 2)=0 then T(n-1, k+1)+T(n-1, k)+T(n-2, k)
                        else T(n+1, k-1)+T(n, k-1)+T(n, k-2)
      fi
    end:
a:= n-> `if`(irem (n, 2)=0, T(1, n), T(n, 1)):
seq(a(n), n=1..30);  # Alois P. Heinz, Feb 08 2011

Mathematica

T[n_, k_] := T[n, k] = Which[n < 1 || k < 1, 0
     , n == 1 && Mod[k, 2] == 1 || k == 1 && Mod[n, 2] == 0, 1
     , Mod[n + k, 2] == 0, T[n - 1, k + 1] + T[n - 1, k] + T[n - 2, k]
     , True,               T[n + 1, k - 1] + T[n, k - 1] + T[n, k - 2]];
a[n_] := If[Mod [n, 2] == 0, T[1, n], T[n, 1]];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 11 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000667, A059216, A063179.

Sequence in context: A174146 A149866 A149867 * A274909 A263308 A288388

Adjacent sequences: A062701 A062702 A062703 * A062705 A062706 A062707

Keyword

easy,nonn

Author

Floor van Lamoen, Jul 11 2001

Extensions

More terms from Alois P. Heinz, Feb 08 2011

Status

approved