A051849 Table in which n-th row gives all compositions of n interpreted as digits in base n+1.

1, 2, 4, 3, 6, 9, 21, 4, 8, 12, 16, 32, 36, 56, 156, 5, 10, 15, 20, 25, 45, 50, 55, 80, 85, 115, 260, 265, 295, 475, 1555, 6, 12, 18, 24, 30, 36, 60, 66, 72, 78, 108, 114, 120, 156, 162, 204, 402, 408, 414, 450, 456, 498, 744, 750, 792, 1086, 2802, 2808, 2850, 3144

Offset

1,2

Comments

All terms on row n are divisible by n. See A051850.

Links

Table of n, a(n) for n=1..61.

Example

n-th row has length 2^(n-1) (A000079[n-1]) 1; 2, 4; 3, 6, 9, 21; 4, 8, 12, 16, 32, 36, 56, 156; 3 can be written as sum like 3, or 1+2 or 2+1 or 1+1+1. Numbers 3, 12, 21 and 111 interpreted in base 4 give the third row of table: 3,6,9,21

Maple

with(combinat); rows_upto_u := proc(u) local a, n; a := []; for n from 1 to u do a := [op(a), op(sort(map(list_in_base_b, map(op, map(permute, partition(n))), (n+1))))]; od; RETURN(a); end; # list_in_base_b given in A051845.

Crossrefs

Cf. A051850, A051851, ...

Cf. A124734.

Sequence in context: A363504 A332878 A113233 * A283961 A333029 A175498

Adjacent sequences: A051846 A051847 A051848 * A051850 A051851 A051852

Keyword

easy,nonn,tabf,base

Author

Antti Karttunen, Dec 13 1999

Extensions

Definition corrected by Franklin T. Adams-Watters, Nov 20 2006

Status

approved