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Smallest number of distinct triangular numbers which sum to n (or -1 if not possible).
1

%I #2 Mar 30 2012 18:51:34

%S 0,1,-1,1,2,-1,1,2,-1,2,1,2,-1,2,3,1,2,3,2,3,4,1,2,-1,2,2,3,2,1,2,3,2,

%T 3,-1,2,3,1,2,2,2,3,3,2,2,3,1,2,3,2,2,3,2,3,3,3,1,2,2,2,3,2,2,3,3,2,2,

%U 1,2,3,2,2,3,2,2,3,3,2,3,1,2,3,2,3,2,2,3,3,2,2,3,3,1,2,2,2,3,3,2,3,2,2,2,2,3,3,1,2,3,2,3,3,2,2,3,2,2,3,3,3,2,1,2,3

%N Smallest number of distinct triangular numbers which sum to n (or -1 if not possible).

%C 20 is the only case where n>3.

%e a(20)=4 since 20=1+3+6+10, a(21)=1 since 21 is triangular, a(22)=2 since 22=1+21, a(23)=-1 since no combination of distinct triangular numbers sum to 23.

%Y Cf. A000217, A002243, A053614, A061208, A061336.

%K sign

%O 0,5

%A _Henry Bottomley_, Apr 25 2001