

A053197


Number of level partitions of n.


1



1, 2, 2, 4, 3, 6, 5, 10, 8, 13, 12, 21, 18, 27, 27, 42, 38, 54, 54, 77, 76, 101, 104, 143, 142, 183, 192, 249, 256, 323, 340, 432, 448, 550, 585, 722, 760, 918, 982, 1190, 1260, 1502, 1610, 1917, 2048, 2408, 2590, 3053, 3264, 3800, 4097, 4765, 5120, 5910, 6378
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OFFSET

1,2


COMMENTS

A partition is level if the powers of 2 dividing its parts are all equal.


LINKS

Table of n, a(n) for n=1..55.


FORMULA

a(n) = Sum_{k=0..A007814(n)} A000009(n/2^k). a(2*n+1) = A000009(2*n+1) = A078408(n).  Vladeta Jovovic, Sep 29 2004


MATHEMATICA

a[n_] := Sum[ PartitionsQ[n/2^k], {k, 0, IntegerExponent[n, 2]}]; Table[ a[n], {n, 1, 55}] (* JeanFrançois Alcover, Dec 12 2011, after Vladeta Jovovic *)


CROSSREFS

Cf. A049313, A053195.
Sequence in context: A060367 A062968 A239966 * A088145 A011754 A090105
Adjacent sequences: A053194 A053195 A053196 * A053198 A053199 A053200


KEYWORD

nonn,nice


AUTHOR

Vladeta Jovovic, Mar 02 2000


STATUS

approved



