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A032006 "AFK" (ordered, size, unlabeled) transform of 2,1,1,1,... 1
1, 2, 1, 5, 5, 7, 19, 21, 33, 41, 101, 109, 175, 231, 321, 623, 761, 1087, 1495, 2109, 2661, 4985, 5849, 8557, 11251, 15831, 20373, 27743, 44357, 55135, 76123, 101373, 136689, 178673, 240125, 303997, 475183, 578271, 793809, 1024991, 1387985, 1763719, 2363671 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of compositions of n into distinct parts if there are 2 kinds of part 1. a(3) = 5: 3, 21, 21', 12, 1'2.

LINKS

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

C. G. Bower, Transforms (2)

MAPLE

b:= proc(n, i, p) option remember;

      `if`(n=0, p!, `if`(i<1, 0, b(n, i-1, p)+

      `if`(i>n, 0, `if`(n=1, 2, 1)*b(n-i, i-1, p+1))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..45);  # Alois P. Heinz, Sep 05 2015

CROSSREFS

Sequence in context: A193536 A152290 A248699 * A167158 A074392 A284428

Adjacent sequences:  A032003 A032004 A032005 * A032007 A032008 A032009

KEYWORD

nonn,changed

AUTHOR

Christian G. Bower

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Sep 05 2015

STATUS

approved

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Last modified February 20 14:37 EST 2018. Contains 299380 sequences. (Running on oeis4.)