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A049798 a(n) = (1/2)*Sum_{k = 1..n} T(n,k), array T as in A049800. 6
0, 0, 0, 1, 0, 2, 2, 2, 3, 7, 2, 7, 10, 8, 8, 15, 11, 19, 16, 15, 22, 32, 19, 25, 34, 34, 33, 46, 33, 47, 47, 48, 61, 65, 45, 62, 77, 79, 68, 87, 74, 94, 97, 86, 105, 127, 98, 114, 120, 124, 129, 154, 141, 151, 142, 147, 172, 200, 151, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

This is also Sum_{k=2..floor((n+1)/2)} ((n+1) mod k). - Lei Zhou, Mar 10 2014

LINKS

Lei Zhou, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A004125(n+1) - A008805(n-2), for n >= 2. - Carl Najafi, Jan 31 2013

a(n) = Sum_{i = 1..ceiling(n/2)} ((n-i+1) mod i). - Wesley Ivan Hurt, Jan 05 2017

EXAMPLE

For n = 3, n+1 = 4, floor((n+1)/2) = 2, mod(4,2) = 0, and so a(3) = 0.

For n = 4, n+1 = 5, floor((n+1)/2) = 2, mod(5,2) = 1, and so a(4) = 1.

...

For n = 12, n+1 = 13, floor((n+1)/2) = 6, mod(13,2) = 1, mod(13,3) = 1, mod(13,4) = 1, mod(13,5) = 3, mod(13,6) = 1, and so a(12) = 1 + 1 + 1 + 3 + 1 = 7.

MAPLE

seq( add( (n+1) mod floor((k+1)/2), k=1..n)/2, n=1..60); # G. C. Greubel, Dec 09 2019

MATHEMATICA

Table[Sum[Mod[n+1, Floor[(k+1)/2]], {k, n}]/2, {n, 60}] (* G. C. Greubel, Dec 09 2019 *)

PROG

(Sage)

def a(n):

    return sum([(n+1)%k for k in range(2, floor((n+3)/2))])

# Ralf Stephan, Mar 14 2014

(PARI) vector(60, n, sum(k=1, n, lift(Mod(n+1, (k+1)\2)) )/2 ) \\ G. C. Greubel, Dec 09 2019

(MAGMA) [ (&+[(n+1) mod Floor((k+1)/2): k in [1..n]])/2: n in [1..60]]; // G. C. Greubel, Dec 09 2019

(GAP) List([1..60], n-> Sum([1..n], k-> (n+1) mod Int((k+1)/2))/2 ); # G. C. Greubel, Dec 09 2019

CROSSREFS

Cf. A004125, A008611, A008805, A049797, A049799, A049801.

Half row sums of A049800.

Sequence in context: A143596 A091712 A125721 * A165198 A245526 A024682

Adjacent sequences:  A049795 A049796 A049797 * A049799 A049800 A049801

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Examples added by Lei Zhou, Mar 10 2014

STATUS

approved

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Last modified July 2 11:54 EDT 2020. Contains 335398 sequences. (Running on oeis4.)