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A080344 Partial sums of A023969. 1
0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 29, 30, 31, 32, 33, 34, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..79.

FORMULA

From Ridouane Oudra, May 11 2019: (Start)

a(n) = (1/2)*(n + 1 - t - abs(n + 1 - t^2)), where t = floor(sqrt(n+1) + 1/2).

a(n) = (1/2)*(n + 1 - A000194(n+1) - abs(n + 1 - A000194(n+1)^2)).

a(n) = (1/2)*(A056847(n+1) - A053188(n+1)). (End)

PROG

(MAGMA) [1/2*(n+1-Floor(Sqrt(n+1)+1/2)-Abs(n+1-(Floor(Sqrt(n+1)+1/2))^2)):n in [0..90]]; // Marius A. Burtea, May 09 2019

(PARI) f(n) = sqrtint(4*n)-2*sqrtint(n); \\ A023969

a(n) = sum(k=0, n, f(k)); \\ Michel Marcus, May 10 2019

CROSSREFS

Cf. A023969.

Sequence in context: A196183 A200264 A104406 * A194225 A025782 A120506

Adjacent sequences:  A080341 A080342 A080343 * A080345 A080346 A080347

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 20 2003

STATUS

approved

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Last modified June 20 09:13 EDT 2021. Contains 345162 sequences. (Running on oeis4.)