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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A221649 Tetrahedron E(n,j,k) = k*T(j,k)*p(n-k), where T(j,k) = 1 if k divides j otherwise 0. 1
1, 1, 1, 2, 2, 1, 2, 1, 0, 3, 3, 2, 4, 1, 0, 3, 1, 0, 2, 4, 5, 3, 6, 2, 0, 6, 1, 0, 2, 4, 1, 0, 0, 0, 5, 7, 5, 10, 3, 0, 9, 2, 4, 0, 8, 1, 0, 0, 0, 5, 1, 2, 3, 0, 0, 6, 11, 7, 14, 5, 0, 15, 3, 6, 0, 12, 2, 0, 0, 0, 10, 1, 2, 3, 0, 0, 6, 1, 0, 0, 0, 0, 0, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The tetrahedron shows a connection between divisors and partitions.

The sum of all elements of slice n is A066186(n).

The sum of row j of slice n is A221529(n,j).

The sum of column k of slice n is A138785(n,k), the sum of all parts of size k in all partitions of n.

See also the tetrahedron of A221650.

LINKS

Table of n, a(n) for n=1..84.

FORMULA

E(n,j,k) = k*A051731(j,k)*A000041(n-j) = A127093(j,k)*A000041(n-j) = k*A221650(n,j,k).

EXAMPLE

First six slices of tetrahedron are

---------------------------------------------------

n  j / k   1  2  3  4  5  6      A221529   A066186

---------------------------------------------------

1  1       1,                       1         1

...................................................

2  1       1,                       1

2  2       1, 2,                    3         4

...................................................

3  1       2,                       2

3  2       1, 2,                    3

3  3       1, 0, 3,                 4         9

...................................................

4  1       3,                       3

4  2       2, 4,                    6

4  3       1, 0, 3,                 4

4  4       1, 2, 0, 4,              7        20

...................................................

5  1       5,                       5

5  2       3, 6,                    9

5, 3,      2, 0, 6,                 8

5, 4,      1, 2, 0, 4,              7

5, 5,      1, 0, 0, 0, 5,           6        35

...................................................

6  1       7,                       7

6  2       5, 10,                  15

6  3       3, 0, 9,                12

6  4       2, 4, 0, 8,             14

6  5       1, 0, 0, 0, 5,           6

6  6       1, 2, 3, 0, 0, 6,       12        66

...................................................

CROSSREFS

Cf. A000005, A000041, A000203, A027750, A051731, A066186, A127093, A138785, A221529, A221650.

Sequence in context: A284478 A298948 A085906 * A090406 A152723 A237497

Adjacent sequences:  A221646 A221647 A221648 * A221650 A221651 A221652

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jan 21 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 September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)