A133610 Partial sums of pyramidal sequence A053616.

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, 34, 34, 35, 37, 40, 44, 47, 49, 50, 50, 51, 53, 56, 60, 64, 67, 69, 70, 70, 71, 73, 76, 80, 85, 89, 92, 94, 95, 95, 96, 98, 101, 105, 110, 115, 119, 122, 124, 125, 125, 126, 128, 131, 135

Offset: 0

Author

Jonathan Vos Post, Dec 28 2007

Keywords

• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A002262, A053188, A053616.

Programs

Haskell

a133610 n = a133610_list !! n
a133610_list = scanl1 (+) a053616_list
-- Reinhard Zumkeller, Jan 24 2014

Formula

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|}.

Extensions

Data corrected by Reinhard Zumkeller, Jan 24 2014