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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.
3
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
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.
Sequence in context: A121708 A286370 A138069 * A367197 A082837 A138115
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Feb 28 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 21 2012
STATUS
approved