Sarah Nibs has authored 3 sequences.
A237585
Number of structures of size n in class A = o x (o + MSET(A)) where o is a neutral structure of size 1.
Original entry on oeis.org
0, 1, 2, 3, 6, 15, 36, 94, 245, 663, 1815, 5062, 14269, 40706, 117103, 339673, 991834, 2913869, 8605576, 25536300, 76096896, 227634717, 683296679, 2057540487, 6213495745, 18813535942, 57103173296, 173710272584, 529534793886, 1617347972250, 4948744120771
Offset: 0
For n = 3 the a(3)=3 pointers are the pointer to the multiset of exactly the pointer to the null pointer, the pointer to the multiset of twice the pointer to the empty multiset, and the pointer to the multiset of exactly the pointer to the multiset of the pointer to the empty multiset.
From _Andrew Howroyd_, Mar 02 2020: (Start)
The a(2) = 2 trees are: 2, (1).
The a(3) = 3 trees are: (2), (11), ((1)).
The a(4) = 6 trees are: ((2)), (12), (111), ((11)), (1(1)), (((1))).
(End)
-
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[1]); for(n=2, n, v=concat([1], EulerT(v)); v[2]++); concat([0],v)} \\ Andrew Howroyd, Mar 02 2020
A200544
Number of distinct bags of distinct sequences of 1s and 2s such that the sum of all terms is n.
Original entry on oeis.org
1, 1, 3, 6, 14, 28, 61, 122, 253, 505, 1017, 2008, 3976, 7769, 15169, 29379, 56751, 108993, 208725, 397913, 756385, 1432578, 2705744, 5094749, 9568504, 17922756, 33492061, 62438472, 116151352, 215612548, 399451325, 738612472, 1363261171, 2511748010, 4620024202
Offset: 0
For n = 4, a(4)=14 and the bags are: 1/1/1/1; 1/1/1,1; 1/1/2; 1/1,1,1; 1/1,2; 1/2,1; 1,1/1,1; 1,1/2; 2/1,1; 2/2; 1,1,1,1; 1,1,2; 1,2,1; 2,1,1.
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- W. S. Gray, K. Ebrahimi-Fard, Affine SISO Feedback Transformation Group and Its Faa di Bruno Hopf Algebra, arXiv:1411.0222 [math.OC], 2014.
- Vaclav Kotesovec, Asymptotics of the Euler transform of Fibonacci numbers, arXiv:1508.01796 [math.CO], Aug 07 2015
- Vaclav Kotesovec, Asymptotics of sequence A034691
- Sarah Nibs, C# code to generate sequence terms
- Wikipedia, Jenga
-
with(numtheory):with(combinat):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
fibonacci(d+1), d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..40); # Alois P. Heinz, Nov 05 2013
-
CoefficientList[Series[Product[1/(1-x^k)^Fibonacci[k+1], {k, 1, 40}], {x, 0, 40}], x] (* Vaclav Kotesovec, Aug 05 2015 *)
-
# uses[EulerTransform from A166861]
a = BinaryRecurrenceSequence(1, 1, 1)
b = EulerTransform(a)
print([b(n) for n in range(35)]) # Peter Luschny, Nov 11 2020
Corrected terms from n=8 and onwards by
Sarah Nibs, Oct 18 2013
C# program corrected and made much more efficient by
Sarah Nibs, Oct 18 2013
A122536
Number of binary sequences of length n with no initial repeats (or, with no final repeats).
Original entry on oeis.org
2, 2, 4, 6, 12, 20, 40, 74, 148, 286, 572, 1124, 2248, 4460, 8920, 17768, 35536, 70930, 141860, 283440, 566880, 1133200, 2266400, 4531686, 9063372, 18124522, 36249044, 72493652, 144987304, 289965744
Offset: 1
a(4)=6: 0100, 0110, 0111, 1000, 1001 and 1011. (But not 00**, 11**, 0101, 1010.)
- Allan Wilks, Table of n, a(n) for n = 1..200 (The first 71 terms were computed by _N. J. A. Sloane_.)
- B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102 [math.CO], 2012-2013.
- B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
- Daniel Gabric, Jeffrey Shallit, Borders, Palindrome Prefixes, and Square Prefixes, arXiv:1906.03689 [cs.DM], 2019.
- Sarah Nibs, Java program for this sequence and A003000
- Index entries for sequences related to curling numbers
See
A121880 for difference from 2^n.
a(31)-a(71) computed from recurrence and the first 30 terms of
A216958 by
N. J. A. Sloane, Sep 28 2012, Oct 25 2012
Comments