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!)
A259841 Number T(n,k) of elements k in all n X n Tesler matrices of nonnegative integers; triangle T(n,k), n>=1, 1<=k<=n, read by rows. 5
1, 3, 1, 15, 5, 2, 117, 37, 17, 7, 1367, 418, 189, 100, 40, 23329, 7027, 3058, 1688, 939, 357, 570933, 171428, 72194, 39274, 24050, 13429, 4820, 19740068, 5948380, 2449366, 1293768, 807576, 517548, 283510, 96030 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the definition of Tesler matrices see A008608.

Sum_{k=1..n} k * T(n,k) = A259787(n).

LINKS

Alois P. Heinz, Rows n = 1..20, flattened

EXAMPLE

There are two 2 X 2 Tesler matrices: [1,0; 0,1], [0,1; 0,2], containing three 1's and one 2, thus row 2 gives [3, 1].

Triangle T(n,k) begins:

:      1;

:      3,      1;

:     15,      5,     2;

:    117,     37,    17,     7;

:   1367,    418,   189,   100,    40;

:  23329,   7027,  3058,  1688,   939,   357;

: 570933, 171428, 72194, 39274, 24050, 13429, 4820;

MAPLE

g:= u-> `if`(u=0, 0, x^u):

b:= proc(n, i, l) option remember; (m->`if`(m=0, [1, g(n)], `if`(i=0,

     (p->p+[0, p[1]*g(n)])(b(l[1]+1, m-1, subsop(1=NULL, l))), add(

     (p->p+[0, p[1]*g(j)])(b(n-j, i-1, subsop(i=l[i]+j, l)))

      , j=0..n))))(nops(l))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(1, n-1, [0$(n-1)])[2]):

seq(T(n), n=1..10);

CROSSREFS

Main diagonal gives A008608(n-1) for n>1.

Column k=1 gives A259843.

Row sums give A259842.

Cf. A259787.

Sequence in context: A121335 A126454 A293558 * A228540 A144815 A065250

Adjacent sequences:  A259838 A259839 A259840 * A259842 A259843 A259844

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jul 06 2015

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 February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)