reviewed

approved

proposed

reviewed

editing

proposed

Cf. A005637, A007111, A261919.

allocated for Andrew HowroydNumber of simple graphs on n unlabeled nodes with minimum degree exactly 2.

0, 0, 1, 2, 8, 43, 360, 4869, 113622, 4605833, 325817259, 40350371693, 8825083057727, 3447229161054412, 2432897732375453872, 3135299553791882831175, 7445569254636418368355175, 32831169277561326131677454356, 270499962116368309216399255404116

1,4

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumVertexDegree.html">Minimum Vertex Degree</a>

a(n) = A261919(n) - A007111(n).

Column k=2 of A294217.

A diagonal of A263293.

Cf. A007111, A261919.

allocated

nonn

Andrew Howroyd, Sep 03 2019

approved

editing

allocated for Andrew Howroyd

recycled

allocated

editing

approved

Starting at n, a(n) is the maximum point visited according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away from zero instead.

0, 1, 2, 3, 21, 26, 6, 6843, 8, 14, 10, 72, 365, 366, 14, 15, 352, 4674389, 18, 22, 891114, 21, 102, 23, 31, 7856204, 26, 27, 28, 1700, 61960674, 3702823, 3702824, 3702825, 3702826, 35, 36, 370, 1047903, 1047904, 596, 41, 42, 43, 2976, 45, 341, 260, 261, 123

0,3

Apparently a duplicate of A248953.

For n=2, the points visited are 2,1,-1,-4,0, the maximum of which is 2, hence a(2) = 2.

(Python)

#Sequences A324660-A324692 generated by manipulating this trip function

#spots - positions in order with possible repetition

#flee - positions from which we move away from zero with possible repetition

#stuck - positions from which we move to a spot already visited with possible repetition

def trip(n):

stucklist = list()

spotsvisited = [n]

leavingspots = list()

turn = 0

forbidden = {n}

while n != 0:

turn += 1

sign = n // abs(n)

st = sign * turn

if n - st not in forbidden:

n = n - st

else:

leavingspots.append(n)

if n + st in forbidden:

stucklist.append(n)

n = n + st

spotsvisited.append(n)

forbidden.add(n)

return {'stuck':stucklist, 'spots':spotsvisited,

'turns':turn, 'flee':leavingspots}

#Actual sequence

def a(n):

d = trip(n)

return max(d['spots'])

Cf. A228474, A324660-A324692.

nonn,new

recycled

David Nacin, Mar 10 2019

reviewed

editing

proposed

reviewed

editing

proposed