login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195223 Number of lower triangles of a 5 X 5 integer array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by n or less and triangles differing by a constant counted only once. 1
111031, 92031109, 9032683465, 289301569283, 4677360495205, 47764170577925, 350767341744137, 2010235691940497, 9496465116615081, 38429133040711965, 136997589911672127, 439401533118090493, 1288688520518224397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 5 of A195220.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..43

FORMULA

Empirical: a(n) = (3508493543/18345600)*n^14 + (3508493543/2620800)*n^13 + (1116775769537/239500800)*n^12 + (422094048023/39916800)*n^11 + (377328209183/21772800)*n^10 + (78475421219/3628800)*n^9 + (1073748492569/50803200)*n^8 + (19848770813/1209600)*n^7 + (221251862417/21772800)*n^6 + (18121075223/3628800)*n^5 + (10435002133/5443200)*n^4 + (505904317/907200)*n^3 + (8793472607/75675600)*n^2 + (1397863/90090)*n + 1.

Since a(n) is an Ehrhart polynomial of degree 14 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 15, it must be correct. - Robert Israel, Oct 06 2019

EXAMPLE

Some solutions for n=5:

  0               0               0               0               0

  2  4            5  2            3  3            1  5            1  4

  7  2  3         1  5  6         5  7  6         2  3  2        -1  0 -1

  5  4  3  7      2  4  1  1      3  8  7  3      5  6  3  0      0  3  0  2

  6  5  6  2  5   5  3  6  3  1   5  3  5  6  2   9  7  2  0  0   5  3 -1  4  3

CROSSREFS

Cf. A195220.

Sequence in context: A146888 A175535 A103874 * A205243 A223110 A094325

Adjacent sequences:  A195220 A195221 A195222 * A195224 A195225 A195226

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 13 2011

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 May 10 14:22 EDT 2021. Contains 343770 sequences. (Running on oeis4.)