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%I #8 Jan 29 2016 11:13:52
%S 0,0,1,1,2,3,3,4,6,7,7,8,10,12,13,13,14,16,19,21,22,22,23,25,28,31,33,
%T 34,34,35,37,40,44,47,49,50,50,51,53,56,60,64,67,69,70,70,71,73,76,80,
%U 85,89,92,94,95,95,96,98,101,105,110,115,119,122,124,125,125,126,128,131,135
%N Partial sums of pyramidal sequence A053616.
%H Reinhard Zumkeller, <a href="/A133610/b133610.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = SUM[i=0..n] distance from i to nearest triangular number = SUM[i=0..n]MIN{|i - (k*(k+1)/2)|} = SUM[i=0..n] MIN{|A000217(i) - i|}.
%o (Haskell)
%o a133610 n = a133610_list !! n
%o a133610_list = scanl1 (+) a053616_list
%o -- _Reinhard Zumkeller_, Jan 24 2014
%Y Cf. A000217, A002262, A053188, A053616.
%K easy,nonn
%O 0,5
%A _Jonathan Vos Post_, Dec 28 2007
%E Data corrected by _Reinhard Zumkeller_, Jan 24 2014
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