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!)
A144528 Triangle read by rows: T(n,k) is the number of trees on n unlabeled nodes with all nodes of degree <= k (n>=1, 0 <= k <= n-1). 8
1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 3, 0, 0, 1, 4, 5, 6, 0, 0, 1, 6, 9, 10, 11, 0, 0, 1, 11, 18, 21, 22, 23, 0, 0, 1, 18, 35, 42, 45, 46, 47, 0, 0, 1, 37, 75, 94, 101, 104, 105, 106, 0, 0, 1, 66, 159, 204, 223, 230, 233, 234, 235, 0, 0, 1, 135, 355, 473, 520, 539, 546, 549, 550, 551 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

R. Neville, Graphs whose vertices are forests with bounded degree, Graph Theory Notes of New York, LIV (2008), 12-21.

EXAMPLE

Triangle begins:

  1

  0 1

  0 0 1

  0 0 1  2

  0 0 1  2  3

  0 0 1  4  5  6

  0 0 1  6  9 10  11

  0 0 1 11 18 21  22  23

  0 0 1 18 35 42  45  46  47

  0 0 1 37 75 94 101 104 105 106

  ...

From Andrew Howroyd, Dec 17 2020: (Start)

Formatted as an array to show the full columns:

================================================

n\k  | 0 1 2   3   4   5   6   7   8   9  10

-----+------------------------------------------

   1 | 1 1 1   1   1   1   1   1   1   1   1 ...

   2 | 0 1 1   1   1   1   1   1   1   1   1 ...

   3 | 0 0 1   1   1   1   1   1   1   1   1 ...

   4 | 0 0 1   2   2   2   2   2   2   2   2 ...

   5 | 0 0 1   2   3   3   3   3   3   3   3 ...

   6 | 0 0 1   4   5   6   6   6   6   6   6 ...

   7 | 0 0 1   6   9  10  11  11  11  11  11 ...

   8 | 0 0 1  11  18  21  22  23  23  23  23 ...

   9 | 0 0 1  18  35  42  45  46  47  47  47 ...

  10 | 0 0 1  37  75  94 101 104 105 106 106 ...

  11 | 0 0 1  66 159 204 223 230 233 234 235 ...

  12 | 0 0 1 135 355 473 520 539 546 549 550 ...

  ...

(End)

PROG

(PARI) \\ here V(n, k) gives column k as a vector.

MSet(p, k)={my(n=serprec(p, x)-1); if(min(k, n)<1, 1 + O(x*x^n), polcoef(exp( sum(i=1, min(k, n), (y^i + O(y*y^k))*subst(p + O(x*x^(n\i)), x, x^i)/i ))/(1-y + O(y*y^k)), k, y))}

V(n, k)={my(g=1+O(x)); for(n=2, n, g=x*MSet(g, k-1)); Vec(1 + x*MSet(g, k) + (subst(g, x, x^2) - g^2)/2)}

M(n, m=n)={Mat(vector(m, k, V(n, k-1)[2..1+n]~))}

{ my(T=M(12)); for(n=1, #T~, print(T[n, 1..n])) } \\ Andrew Howroyd, Dec 18 2020

CROSSREFS

Columns k=2..6 are A000012, A000672, A000602, A036650, A036653.

The last three diagonals give A144527, A144520, A000055.

Cf. A144215, A238414, A299038.

Sequence in context: A123679 A167948 A111755 * A290694 A146164 A263141

Adjacent sequences:  A144525 A144526 A144527 * A144529 A144530 A144531

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Dec 20 2008

EXTENSIONS

a(53) corrected and terms a(56) and beyond from Andrew Howroyd, Dec 17 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 18 03:03 EDT 2021. Contains 343994 sequences. (Running on oeis4.)