OFFSET
1,3
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
EXAMPLE
Triangle begins:
1
0 2
1 2 5
0 2 4 8
1 3 7 10 15
0 4 8 14 18 24
1 4 12 19 27 32 39
0 4 12 24 34 44 50 58
1 5 18 32 49 62 74 81 90
0 6 18 40 60 82 98 112 120 130
1 6 24 49 81 108 135 154 170 179 190
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [`if`(k=0, 1, 0), 0],
`if`(i<1 or k=0, [0$2], ((f, g)-> f+g+[0, `if`(irem(i, 2)=1,
g[1], 0)])(b(n, i-1, k), `if`(i>n, [0$2], b(n-i, i, k-1)))))
end:
T:= proc(n, k) T(n, k):= b(n$2, k)[2]+`if`(k=1, 0, T(n, k-1)) end:
seq(seq(T(n, k), k=1..n), n=1..14); # Alois P. Heinz, Aug 04 2014
MATHEMATICA
Grid[Table[Sum[Sum[Count[Flatten[IntegerPartitions[n, {j}]], i], {i, 1, n, 2}], {j, k}], {n, 11}, {k, n}]]
(* second program: *)
b[n_, i_, k_] := b[n, i, k] = If[n == 0, {If[k == 0, 1, 0], 0}, If[i < 1 || k == 0, {0, 0}, Function[{f, g}, f + g + {0, If[Mod[i, 2] == 1, g[[1]], 0]}][b[n, i - 1, k], If[i > n, {0, 0}, b[n - i, i, k - 1]]]]];
T[n_, k_] := b[n, n, k][[2]];
Table[Table[T[n, k], {k, 1, n}] // Accumulate, {n, 1, 14}] // Flatten (* Jean-François Alcover, Jul 21 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Aug 03 2014
STATUS
approved