

A224957


Number of compositions [p(1), p(2), ..., p(k)] of n such that p(j) <= 2*p(j1) and p(j1) <= 2*p(j).


16



1, 1, 2, 4, 6, 11, 19, 31, 54, 92, 154, 266, 454, 771, 1319, 2249, 3834, 6550, 11176, 19069, 32558, 55567, 94838, 161891, 276325, 471659, 805102, 1374234, 2345724, 4004031, 6834605, 11666260, 19913668, 33991462, 58021534, 99039592, 169055094, 288567886, 492569833, 840790082
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OFFSET

0,3


LINKS



EXAMPLE

There are a(6) = 19 such compositions of 6:
01: [ 1 1 1 1 1 1 ]
02: [ 1 1 1 1 2 ]
03: [ 1 1 1 2 1 ]
04: [ 1 1 2 1 1 ]
05: [ 1 1 2 2 ]
06: [ 1 2 1 1 1 ]
07: [ 1 2 1 2 ]
08: [ 1 2 2 1 ]
09: [ 1 2 3 ]
10: [ 2 1 1 1 1 ]
11: [ 2 1 1 2 ]
12: [ 2 1 2 1 ]
13: [ 2 2 1 1 ]
14: [ 2 2 2 ]
15: [ 2 4 ]
16: [ 3 2 1 ]
17: [ 3 3 ]
18: [ 4 2 ]
19: [ 6 ]


MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, add(
b(nj, j), j=`if`(i=0, 1..n, ceil(i/2)..min(n, 2*i))))
end:
a:= n> b(n, 0):


MATHEMATICA

Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@Table[#[[i]]<=2*#[[i1]]&&#[[i1]]<=2*#[[i]], {i, 2, Length[#]}]&]], {n, 15}] (* Gus Wiseman, Mar 12 2021 *)
b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[b[n  j, j], {j, If[i == 0, Range[n], Range[Ceiling[i/2], Min[n, 2*i]]]}]];
a[n_] := b[n, 0];


CROSSREFS

A000929 counts partitions with adjacent parts x >= 2y.
A002843 counts compositions with adjacent parts x <= 2y.
A045690 counts sets with maximum n with adjacent elements y < 2x.
A154402 counts partitions with adjacent parts x = 2y.
A274199 counts compositions with adjacent parts x < 2y.
A342094 counts partitions with adjacent parts x <= 2y (strict: A342095).
A342098 counts partitions with adjacent parts x > 2y.
A342331 counts compositions with adjacent parts x = 2y or y = 2x.
A342332 counts compositions with adjacent parts x > 2y or y > 2x.
A342333 counts compositions with adjacent parts x >= 2y or y >= 2x.
A342334 counts compositions with adjacent parts x >= 2y or y > 2x.
A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
A342336 counts compositions with adjacent parts x > 2y or y = 2x.
A342337 counts partitions with adjacent parts x = y or x = 2y.
A342338 counts compositions with adjacent parts x < 2y and y <= 2x.
A342340 counts compositions with adjacent x = y or x = 2y or y = 2x.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



