A227552 Number of partitions of n into distinct parts with maximal boundary size.

1, 1, 1, 1, 1, 2, 3, 1, 2, 2, 4, 6, 1, 1, 3, 4, 6, 9, 14, 1, 2, 3, 5, 8, 11, 17, 24, 1, 1, 3, 5, 8, 11, 18, 24, 35, 49, 1, 2, 3, 6, 9, 14, 21, 30, 42, 60, 81, 1, 1, 3, 5, 9, 13, 21, 29, 43, 60, 84, 113, 156, 1, 2, 3, 6, 10, 15, 24, 35, 50, 71, 99, 134, 184, 246

Offset

0,6

Comments

The boundary size is the number of parts having less than two neighbors.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A227551(n,A227568(n)).

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>1, x, 1),
      expand(`if`(i<1, 0, `if`(t>1, x, 1)*b(n, i-1, iquo(t, 2))+
      `if`(i>n, 0, `if`(t=2, x, 1)*b(n-i, i-1, iquo(t, 2)+2)))))
    end:
a:= n-> (p->coeff(p, x, degree(p)))(b(n$2, 0)):
seq(a(n), n=0..100);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t>1, x, 1], Expand[If[i<1, 0, If[t>1, x, 1]*b[n, i-1, Quotient[t, 2]] + If[i>n, 0, If[t==2, x, 1] * b[n-i, i-1, Quotient[t, 2]+2]]]]]; a[n_] := Function [p, Coefficient[p, x, Exponent[p, x]]][b[n, n, 0]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Crossrefs

Last elements of rows of A227551.

Last nonzero elements of rows of A227345.

Cf. A053993, A201077.

Sequence in context: A366294 A351441 A254761 * A205003 A159956 A053839

Adjacent sequences: A227549 A227550 A227551 * A227553 A227554 A227555

Keyword

nonn

Author

Alois P. Heinz, Jul 16 2013

Status

approved