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A227552 Number of partitions of n into distinct parts with maximal boundary size. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A244232 A227781 A254761 * A205003 A159956 A053839

Adjacent sequences:  A227549 A227550 A227551 * A227553 A227554 A227555

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 16 2013

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)