The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A026835 Triangular array read by rows: T(n,k) = number of partitions of n into distinct parts in which every part is >=k, for k=1,2,...,n. 7
 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 4, 2, 1, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 6, 3, 2, 1, 1, 1, 1, 1, 8, 5, 3, 2, 1, 1, 1, 1, 1, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1, 12, 7, 4, 3, 2, 1, 1, 1, 1, 1, 1, 15, 8, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1, 18, 10, 6, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 22, 12, 7, 4, 3, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS T(n,1)=A000009(n), T(n,2)=A025147(n) for n>1, T(n,3)=A025148(n) for n>2, T(n,4)=A025149(n) for n>3. A219922(n) = smallest number of row containing n. - Reinhard Zumkeller, Dec 01 2012 LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened FORMULA G.f.: Sum_{k>=1} (y^k*(-1+Product_{i>=k} (1+x^i))). - Vladeta Jovovic, Aug 25 2003 T(n, k) = 1 + Sum(T(i, j): i>=j>k and i+j=n+1). - Reinhard Zumkeller, Jan 01 2003 T(n, k) > 1 iff 2*k < n. - Reinhard Zumkeller, Jan 01 2003 EXAMPLE From Michael De Vlieger, Aug 03 2020: (Start) Table begins:    1    1   1    2   1   1    2   1   1   1    3   2   1   1   1    4   2   1   1   1   1    5   3   2   1   1   1   1    6   3   2   1   1   1   1   1    8   5   3   2   1   1   1   1   1   10   5   3   2   1   1   1   1   1   1   12   7   4   3   2   1   1   1   1   1   1   15   8   5   3   2   1   1   1   1   1   1   1   ... (End) MATHEMATICA Nest[Function[{T, n, r}, Append[T, Table[1 + Total[T[[##]] & @@@ Select[r, #[[-1]] > k + 1 &]], {k, 0, n}]]] @@ {#1, #2, Transpose[1 + {#2 - #3, #3}]} & @@ {#1, #2, Range[Ceiling[#2/2] - 1]} & @@ {#, Length@ #} &, {{1}}, 12] // Flatten (* Michael De Vlieger, Aug 03 2020 *) PROG (Haskell) import Data.List (tails) a026835 n k = a026835_tabl !! (n-1) !! (k-1) a026835_row n = a026835_tabl !! (n-1) a026835_tabl = map    (\row -> map (p \$ last row) \$ init \$ tails row) a002260_tabl    where p 0      _ = 1          p _     [] = 0          p m (k:ks) = if m < k then 0 else p (m - k) ks + p m ks -- Reinhard Zumkeller, Dec 01 2012 CROSSREFS Cf. A026807. Cf. A002260, A060016. Sequence in context: A177994 A179285 A079211 * A117975 A143258 A027199 Adjacent sequences:  A026832 A026833 A026834 * A026836 A026837 A026838 KEYWORD nonn,tabl AUTHOR 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)