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 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, 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)