login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111490 Antidiagonal sums of the numerical array defined by M(n,k) = 1 + (k-1) mod n. 22
1, 2, 4, 5, 9, 9, 15, 16, 21, 23, 33, 29, 41, 45, 51, 52, 68, 65, 83, 81, 91, 99, 121, 109, 128, 138, 152, 152, 180, 168, 198, 199, 217, 231, 253, 234, 270, 286, 308, 298, 338, 326, 368, 372, 384, 404, 450, 422, 463, 470, 500, 506, 558, 546, 584, 576, 610, 636 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Previous name was "Sum of the element of the antidiagonals of the numerical array M(m,n) defined as follows. First row (M11, M12, ..., M1n): 1, 1, 1, 1, 1, 1, ... (all 1's). Second row (M21, M22, ..., M2n): 1, 2, 1, 2, 1, 2, ... (sequence 1, 2 repeated). Third row (M31, M32, ..., M3n): 1, 2, 3, 1, 2, 3, 1, 2, 3, ... (sequence 1, 2, 3 repeated). Fourth row (M41, M42, ..., M4n): 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, ... (sequence 1, 2, 3, 4 repeated). And so on."

Then the sequence is M(1,1), M(1,2) + M(2,1), M(1,3) + M(2,2) + M(3,1), etc., a(n) = Sum_{i=1..n} M(i, n-i+1).

The successive determinants of the arrays are the factorial numbers (A000142). - Robert G. Wilson v

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n + A004125(n). - Juri-Stepan Gerasimov, Aug 30 2009

a(n) = Sum_{i=1..n+1} (n mod i). - Wesley Ivan Hurt, Dec 05 2014

G.f.: 2*x/(1-x)^3 - (1-x)^(-1)*Sum_{k>=1} k*x^k/(1-x^k). - Robert Israel, Oct 11 2015

EXAMPLE

Considering the 6 X 6 array:

1, 1, 1, 1, 1, 1

1, 2, 1, 2, 1, 2

1, 2, 3, 1, 2, 3

1, 2, 3, 4, 1, 2

1, 2, 3, 4, 5, 1

1, 2, 3, 4, 5, 6

The third element of the sequence is 1+2+1=4.

The fifth element of the sequence is 1+2+3+2+1=9.

MAPLE

A111490:=n->add(n mod i, i=1..n+1): seq(A111490(n), n=1..100); # Wesley Ivan Hurt, Dec 05 2014

MATHEMATICA

t = Table[Flatten@Table[Range@n, {m, Ceiling[99/n]}], {n, 99}]; f[n_] := Sum[ t[[i, n - i + 1]], {i, n}]; Array[f, 58] (* Robert G. Wilson v, Nov 22 2005 *)

(* to view table *) Table[Flatten@Table[Range@n, {m, Ceiling[40/n]}], {n, 10}] // TableForm

PROG

(PARI) vector(100, n, n + sum(k=2, n, n % k)) \\ Altug Alkan, Oct 12 2015

(PARI) a(n) = sum(k=1, n, 2*k-sigma(k)); \\ Michel Marcus, Oct 11 2015

CROSSREFS

Cf. A000142, A004125.

Partial sums of A033879. - Gionata Neri, Sep 10 2015

Sequence in context: A167511 A242398 A174112 * A079784 A189210 A188969

Adjacent sequences:  A111487 A111488 A111489 * A111491 A111492 A111493

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Nov 21 2005

EXTENSIONS

Edited and extended by Robert G. Wilson v, Nov 22 2005

Name changed by Michel Marcus, Sep 23 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)