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!)
A334377 Irregular triangle read by rows: T(n,k) is the number of partitions of k into distinct parts p such that 2 <= p <= n. 0
1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 3, 2, 4, 3, 4, 4, 4, 4, 4, 4, 3, 4, 2, 3, 2, 2, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,25

LINKS

Table of n, a(n) for n=2..84.

FORMULA

G.f. for row n: Product_{i=2..n} (1+x^i), n >= 2.

EXAMPLE

Irregular triangle begins:

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

n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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

  2 | 1 0 1

  3 | 1 0 1 1 0 1

  4 | 1 0 1 1 1 1 1 1 0 1

  5 | 1 0 1 1 1 2 1 2 1 2  1  1  1  0  1

  6 | 1 0 1 1 1 2 2 2 2 3  2  3  2  2  2  2  1  1  1  0  1

  ...

For n = 4: T(4,3) = 1 because we have [3], G.f.=1+x^2+x^3+x^4+x^5+x^6+x^7+x^9;

For n = 5: T(5,5) = 2 because we have [5] and [3,2].

G.f. is 1+x^2+x^3+x^4+2x^5+x^6+2x^7+x^8+2x^9+x^10+x^11+x^12+x^14.

MATHEMATICA

trow[n_] := CoefficientList[Product[(1 + x^i), {i, 2, n}], x]; nmax = 10; Table[trow[n], {n, 2, nmax}] // Flatten

CROSSREFS

Cf. A000009, A000041, A025147, A087897, A334305.

Sequence in context: A214339 A129174 A129175 * A063053 A063050 A330098

Adjacent sequences:  A334374 A334375 A334376 * A334378 A334379 A334380

KEYWORD

tabf,nonn,easy

AUTHOR

Victor Mishnyakov, Elena Lanina, Apr 25 2020

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 15 01:24 EDT 2021. Contains 343909 sequences. (Running on oeis4.)