This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A245842 Triangle T read by rows: T(n,k) = Total number of even parts in all partitions of n with exactly k parts, 1 <= k <= n. 4
 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 2, 2, 1, 0, 1, 2, 5, 2, 1, 0, 0, 3, 4, 5, 2, 1, 0, 1, 4, 7, 8, 5, 2, 1, 0, 0, 4, 8, 10, 8, 5, 2, 1, 0, 1, 4, 12, 14, 15, 8, 5, 2, 1, 0, 0, 5, 12, 19, 18, 15, 8, 5, 2, 1, 0, 1, 6, 18, 24, 27, 24, 15, 8, 5, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Column sequences appear to converge to A066897. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA T(n,k) + A245840(n,k) = A172467(n,k). EXAMPLE Triangle begins 0 1  0 0  1   0 1  2   1   0 0  2   2   1   0 1  2   5   2   1   0 0  3   4   5   2   1  0 1  4   7   8   5   2  1  0 0  4   8  10   8   5  2  1  0 1  4  12  14  15   8  5  2  1  0 0  5  12  19  18  15  8  5  2  1  0 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)=0,        g[1], 0)])(b(n, i-1, k), `if`(i>n, [0\$2], b(n-i, i, k-1)))))     end: T:= (n, k)-> b(n\$2, k)[2]: seq(seq(T(n, k), k=1..n), n=1..14);  # Alois P. Heinz, Aug 04 2014 MATHEMATICA Grid[Table[Sum[Count[Flatten[IntegerPartitions[n, {k}]], i], {i, 2, n, 2}], {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] == 0, 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}], {n, 1, 14}] // Flatten (* Jean-François Alcover, May 21 2016, after Alois P. Heinz *) CROSSREFS Cf. A245843 (partial sums of row entries). Cf. A066898 (row sums), A172467. Cf. A245840, A245841. Sequence in context: A258278 A122856 A055791 * A300574 A191400 A168315 Adjacent sequences:  A245839 A245840 A245841 * A245843 A245844 A245845 KEYWORD nonn,tabl AUTHOR L. Edson Jeffery, Aug 03 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)