A051849 -id:A051849 - cp's OEIS frontend

A051850 a(n) = A051849(n)/floor(log_2(n)+1).

1, 1, 2, 1, 2, 3, 7, 1, 2, 3, 4, 8, 9, 14, 39, 1, 2, 3, 4, 5, 9, 10, 11, 16, 17, 23, 52, 53, 59, 95, 311, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 18, 19, 20, 26, 27, 34, 67, 68, 69, 75, 76, 83, 124, 125, 132, 181, 467, 468, 475, 524, 867, 3268, 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15

Offset: 1

Antti Karttunen, Dec 13 1999

			n-th row has length 2^(n-1) (A000079[n-1]) 1; 1,2; 1,2,3,7; 1,2,3,4,8,9,14,39; 1,2,3,4,5,9,10,11,16,17,23,52,53,59,95,311;

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,map(op,map(permute,partition(n))),(n+1))), n))]; od; RETURN(a); end; divby := (n,d) -> n/d;

A051851 Table in which n-th row gives all partitions of n interpreted in base n+1. (A subset of A051849 with each term having a non-descending digit-sequence in base n+1).

Original entry on oeis.org

1, 2, 4, 3, 6, 21, 4, 8, 12, 32, 156, 5, 10, 15, 45, 50, 260, 1555, 6, 12, 18, 24, 60, 66, 114, 402, 408, 2802, 19608, 7, 14, 21, 28, 77, 84, 91, 147, 588, 595, 658, 4683, 4690, 37450, 299593, 8, 16, 24, 32, 40, 96, 104, 112, 184, 192, 824, 832, 840, 912, 1640

Offset: 1

Antti Karttunen, Dec 13 1999

All terms on row n are divisible by n (see A051852).

			Rows have lengths 1,2,3,5,7,11,15, etc. (A000041(n)). Terms: 1; 2, 4; 3, 6, 21; 4, 8, 12, 32, 156; 5, 10, 15, 45, 50, 260, 1555;

A subset of A051849.

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,partition(n),(n+1))))]; od; RETURN(a); end; # list_in_base given in A051845.

cp's OEIS Frontend

A051850 a(n) = A051849(n)/floor(log_2(n)+1).

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