A262496 Number of partitions of n into parts of sorts {1, 2, ... } which are introduced in ascending order such that sorts of adjacent parts are different.

1, 1, 2, 4, 10, 27, 87, 312, 1269, 5703, 28082, 149643, 855938, 5217753, 33712046, 229799508, 1646314498, 12355371024, 96861186897, 791258791159, 6720627161903, 59234364141343, 540812222291531, 5106663817387466, 49798678281320763, 500857393909589995

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Example

a(3) = 4: 3a, 2a1b, 1a1b1a, 1a1b1c (in this example the sorts are labeled a, b, c).

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
    end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
T:= (n, k)->  add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> add(T(n, k), k=0..n):
seq(a(n), n=0..30);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n==0 || i==1, k^(n-1), b[n, i-1, k] + If[i > n, 0, k*b[n-i, i, k]]]; A[n_, k_] := If[n==0, 1, If[k<2, k, k*b[n, n, k - 1]]]; T[n_, k_] := Sum[A[n, k-i]*(-1)^i/(i!*(k-i)!), {i, 0, k}]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *)

Crossrefs

Row sums of A262495.

Cf. A258466.

Sequence in context: A148107 A148108 A057786 * A007776 A268522 A123428

Adjacent sequences: A262493 A262494 A262495 * A262497 A262498 A262499

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2015

Status

approved