0,2

The sequence is not monotonous.

m=a^2+b^3, a,b>0.

a(0)=1 because there's no partition of 1 to square and cube;

a(1)=2 because 2=1^2+1^3, one partition;

a(2)=17 because 17=3^2+2^3=4^2+1^3, two partitions;

a(3)=1737 because {1737=3^2+12^3=35^2+8^3=39^2+6^3,

three partitions, etc.

Table of partitions:

{m,{a_i,b_i}}

{1,{-}}

{2,{1,1}}

{17,{3,2},{4,1}}

{1737,{3,12},{35,8},{39,6}}

{1025,{5,10},{30,5},{31,4},{32,1}}

{92025,{30,45},{152,41},{213,36},{255,30},{303,6}}

{3375900,{30,150},{1430,110},{1551,99},{1794,54},{1830,30},{1837,11}}

{11530025,{858,221},{2280,185},{3055,130},{3245,100},{3271,94},{3362,61},{3393,26}}

Cf. A123388.

Sequence in context: A058233 A062635 A060835 this_sequence A092415 A060353 A002814

Adjacent sequences: A122051 A122052 A122053 this_sequence A122055 A122056 A122057

nonn

Zak Seidov (zakseidov(AT)yahoo.com), Oct 15 2006