OFFSET
1,2
COMMENTS
Antidiagonal sum of below array:
1, 1, 1, 1, 1, 1, ... (1-bonacci numbers)
1, 1, 2, 3, 5, 8, ... (2-bonacci or Fibonacci numbers)
1, 1, 1, 3, 5, 9, ... (3-bonacci or tribonacci numbers)
1, 1, 1, 1, 4, 7, ... (4-bonacci or tetranacci numbers)
...
FORMULA
a(n) = Sum_{i=1..n} of nac(i,n-i+1) = Sum_{i=1..n} of nac(n-i+1,i).
MAPLE
b:= proc(i, n) option remember; `if`(n=0, 0,
`if`(n<=i, 1, add(b(i, n-j), j=1..i)))
end:
a:= n-> add(b(i+1, n-i), i=0..n):
seq(a(n), n=1..37); # Alois P. Heinz, Jun 21 2021
MATHEMATICA
b[i_, n_] := b[i, n] = If[n == 0, 0, If[n <= i, 1, Sum[b[i, n - j], {j, 1, i}]]];
a[n_] := Sum[b[i + 1, n - i], {i, 0, n}];
Table[a[n], {n, 1, 37}] (* Jean-François Alcover, Dec 27 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christoph B. Kassir, Jun 21 2021
STATUS
approved