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

0,5

Links

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

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|}.

Prog

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

Crossrefs

Cf. A000217, A002262, A053188, A053616.

Sequence in context: A023158 A120882 A102187 * A256211 A265109 A301277

Adjacent sequences: A133607 A133608 A133609 * A133611 A133612 A133613

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 28 2007

Extensions

Data corrected by Reinhard Zumkeller, Jan 24 2014

Status

approved