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A006897 Hierarchical linear models on n factors allowing 2-way interactions; or graphs with <= n nodes.
(Formerly M1153)
2
1, 2, 4, 8, 19, 53, 209, 1253, 13599, 288267, 12293435, 1031291299, 166122463891, 50668153831843, 29104823811067331, 31455590793615376099, 64032471295321173271027 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The subsequence of primes begins: 2, 19, 53, 166122463891, 29104823811067331. - Jonathan Vos Post, Feb 14 2010

a(n) is the number of isolated points over all simple unlabelled graphs with (n+1) nodes. - Geoffrey Critzer, Apr 14 2012

REFERENCES

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..16.

FORMULA

O.g.f.: A(x)/(1-x) where A(x) is o.g.f. for A000088. -Geoffrey Critzer, Apr 12 2012

EXAMPLE

a(2)=4 includes null graph [], G1=[o], G2=[o o], G3=[o-o].

MATHEMATICA

nn = 15; g = Sum[NumberOfGraphs[n] x^n, {n, 0, nn}]; CoefficientList[Series[g/(1 - x), {x, 0, nn}], x]  (* Geoffrey Critzer, Apr 12 2012 *)

CROSSREFS

Partial sums of A000088.

Sequence in context: A173310 A320178 A128816 * A287025 A034767 A005518

Adjacent sequences:  A006894 A006895 A006896 * A006898 A006899 A006900

KEYWORD

easy,nonn,nice

AUTHOR

Colin Mallows

STATUS

approved

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Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)