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 A027356 Array read by rows: T(n,k) = number of partitions of n into distinct odd parts in which k is the greatest part, for k=1,2,...,n, n>=1. 6
 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,145 COMMENTS First T(n,k) not 0 or 1 is T(17,9)=2, which counts 1+7+9 and 3+5+9. Row sums: A000700. LINKS Alois P. Heinz, Rows n = 1..361, flattened Sean A. Irvine, Java program (github) FORMULA T(n, 1)=0 for all n; T(n, n)=1 for all odd n>1; and for n>=3, T(n, k)=0 if k is even, else T(n, k)=Sum{T(n-k, i): i=1, 2, ..., n-1} for k=2, 3, ..., n-1. EXAMPLE First 5 rows: 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 Row 40 with even-numbered terms deleted: 0 0 0 0 0 0 2 5 6 7 6 5 4 3 2 1 1 1 1; E.g. final 2 counts these two partitions: 9+31 and 1+3+5+31. MAPLE b:= proc(n, i) option remember; `if`(n>i^2, 0, `if`(n=0, 1, b(n, i-1) +(p-> `if`(p>n, 0, b(n-p, i-1)))((2*i-1)))) end: T:= (n, k)-> `if`(k::even, 0, b(n-k, (k-1)/2)): seq(seq(T(n, k), k=1..n), n=1..20); # Alois P. Heinz, Oct 28 2019 MATHEMATICA b[n_, i_] := b[n, i] = If[n > i^2, 0, If[n == 0, 1, b[n, i - 1] + Function[p, If[p > n, 0, b[n - p, i - 1]]][2i - 1]]]; T [n_, k_] := If[EvenQ[k], 0, b[n - k, (k - 1)/2]]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 20}] // Flatten (* Jean-François Alcover, Dec 06 2019, after Alois P. Heinz *) CROSSREFS Cf. A000700. T(4n+1,2n+1) gives A069910. Sequence in context: A173856 A288926 A373840 * A361114 A181663 A359370 Adjacent sequences: A027353 A027354 A027355 * A027357 A027358 A027359 KEYWORD nonn,tabl AUTHOR Clark Kimberling, revised Jul 23 2004 EXTENSIONS Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified September 7 23:15 EDT 2024. Contains 375749 sequences. (Running on oeis4.)