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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).
5
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
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
KEYWORD
easy,nonn
AUTHOR
Floor van Lamoen, Jul 11 2001
EXTENSIONS
More terms from Alois P. Heinz, Feb 08 2011
STATUS
approved