A171601 The largest part in the set of all {x,y,z} for any partitioning n=x+y+z into three triangular numbers x, y and z.

1, 1, 3, 3, 3, 6, 6, 6, 6, 10, 10, 10, 10, 10, 15, 15, 15, 15, 15, 10, 21, 21, 21, 21, 21, 15, 21, 28, 28, 28, 28, 28, 21, 28, 28, 36, 36, 36, 36, 36, 28, 36, 36, 28, 45, 45, 45, 45, 45, 28, 45, 45, 28, 45, 55, 55, 55, 55, 55, 45, 55, 55, 45, 55, 55, 66, 66, 66, 66, 66, 55, 66

Offset

1,3

Comments

Write down all possible n=A000217(i)+A000217(j)+A000217(k) with 0<=i<=j<=k and set a(n) to the maximum term found on the right hand sides.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

n=8: 8=1+1+6 =A000217(1)+A000217(1)+A000217(3), admits only one partitioning, so a(8)=max(1,6)=6.
n=17: 17 = 1+1+15 = 1+6+10. a(17) = max(1,15,6,10) = 15.
n=18: 18= 0+3+15 = 6+6+6. a(18) = max(0,3,15,6) = 15.
n=20: 20= 0+10+10 (one partitioning only), a(20)= max(0,10)=10.
n=21: 21= 1+10+10 = 0+0+21 = 0+6+15 = 3+3+15. a(21) = max(1,10,0,21,6,15,3) = 21.

Mathematica

a[n_] := Max@ Flatten@ IntegerPartitions[ n, {3}, (# (# + 1)/2) & /@ Range[0, Sqrt[8*n + 1]/2]]; Array[a, 100] (* Giovanni Resta, May 12 2016 *)

Crossrefs

Sequence in context: A133774 A108581 A073080 * A057944 A281258 A080607

Adjacent sequences: A171598 A171599 A171600 * A171602 A171603 A171604

Keyword

easy,nonn

Author

Tanya Khovanova and R. J. Mathar, Dec 12 2009

Status

approved