A051850 -id:A051850 - cp's OEIS frontend

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

Antti Karttunen, Dec 13 1999

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

			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

Cf. A051850, A051851, ...

Cf. A124734.

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.

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

A051852 A051851(n)/row_index_of(n).

Original entry on oeis.org

1, 1, 2, 1, 2, 7, 1, 2, 3, 8, 39, 1, 2, 3, 9, 10, 52, 311, 1, 2, 3, 4, 10, 11, 19, 67, 68, 467, 3268, 1, 2, 3, 4, 11, 12, 13, 21, 84, 85, 94, 669, 670, 5350, 42799, 1, 2, 3, 4, 5, 12, 13, 14, 23, 24, 103, 104, 105, 114, 205, 923, 924, 934, 8304, 8305, 74734, 672605, 1, 2, 3

Offset: 1

Antti Karttunen, Dec 13 1999

			1; 1, 2; 1, 2, 7; 1, 2, 3, 8, 39; 1, 2, 3, 9, 10, 52, 311;

A subset of A051850 (but note the relative indexing...)

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

cp's OEIS Frontend

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

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