A208475 Triangle read by rows: T(n,k) = total sum of odd/even parts >= k in all partitions of n, if k is odd/even.

1, 2, 2, 7, 2, 3, 10, 10, 3, 4, 23, 12, 11, 4, 5, 36, 30, 17, 14, 5, 6, 65, 40, 35, 18, 17, 6, 7, 94, 82, 49, 44, 22, 20, 7, 8, 160, 110, 93, 58, 48, 26, 23, 8, 9, 230, 190, 133, 108, 70, 56, 30, 26, 9, 10, 356, 260, 217, 148, 124, 76, 64, 34, 29, 10, 11

Offset

1,2

Comments

Essentially this sequence is related to A206561 in the same way as A206563 is related to A181187. See the calculation in the example section of A206563.

Links

Alois P. Heinz, Rows n = 1..141, flattened

Example

Triangle begins:
1;
2,   2;
7,   2,  3;
10, 10,  3,  4;
23, 12, 11,  4,  5;
36, 30, 17, 14,  5,  6;

Maple

p:= (f, g)-> zip((x, y)-> x+y, f, g, 0):
b:= proc(n, i) option remember; local f, g;
      if n=0 then [1]
    elif i=1 then [1, n]
    else f:= b(n, i-1); g:= `if`(i>n, [0], b(n-i, i));
         p (p (f, g), [0$i, g[1]])
      fi
    end:
T:= proc(n) local l;
      l:= b(n, n);
      seq (add (l[i+2*j+1]*(i+2*j), j=0..(n-i)/2), i=1..n)
    end:
seq (T(n), n=1..14);  # Alois P. Heinz, Mar 21 2012

Mathematica

p[f_, g_] := With[{m = Max[Length[f], Length[g]]}, PadRight[f, m, 0] + PadRight[g, m, 0]]; b[n_, i_] := b[n, i] = Module[{f, g}, Which[n == 0, {1}, i == 1, {1, n}, True, f = b[n, i-1]; g = If[i>n, {0}, b[n-i, i]]; p[p[f, g], Append[Array[0&, i], g[[1]]]]]]; T[n_] := Module[{l}, l = b[n, n]; Table[Sum[l[[i+2j+1]]*(i+2j), {j, 0, (n-i)/2}], {i, 1, n}]]; Table[T[n], {n, 1, 14}] // Flatten (* Jean-François Alcover, Mar 11 2015, after Alois P. Heinz *)

Crossrefs

Column 1-2: A066967, A066966. Right border is A000027.

Cf. A138785, A181187, A206561, A206563, A208476.

Sequence in context: A121708 A286370 A138069 * A367197 A082837 A138115

Adjacent sequences: A208472 A208473 A208474 * A208476 A208477 A208478

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 28 2012

Extensions

More terms from Alois P. Heinz, Mar 21 2012

Status

approved