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A058227 Number of edges in all simple (loopless) paths, connecting any node with all the remaining ones in optimal graphs of degree 4. 0
4, 28, 112, 352, 972, 2484, 6040, 14200 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Number of edges occurring in all simple, loopless paths, connecting any node with all the remaining ones forming optimal graphs degree of 4, (2*d(G)^2+2*d(G)+1, 2*d(G)+1) with d(G) denoting graph diameter.
REFERENCES
R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley company, 1994.
LINKS
FORMULA
a(n) = d(V)*Sum_{k=1..d(G)} k*(2^k-1) where d(V) is graph degree, and d(G) is graph diameter a(n)=d(V)*array(1..d(G))*array(1..(2^d(G)-1));
Conjectures from Sean A. Irvine, Jul 29 2022: (Start)
a(n) = 4 * Sum_{k=1..n} k*(2^k-1).
a(n) = (8*n-8)*2^n - 2*n^2 - 2*n + 8.
a(n) = a(n-1) + 4*n*(2^n-1) with a(0)=0.
(End)
EXAMPLE
a(5)=4(1+2*3+3*7+4*15+5*31)=972 S := array(1..5,[1,2,3,4,5]); T := array(1..5,[1,3,7,15,31]); a(5) := evalm(S&*T); a(5) := 243
MAPLE
d(V) := 4; n := 5; a(n) := d(V)*sum('n*(2^n-1)', 'n'=1..n); or d(V) := 4; S := array(1..5, [1, 2, 3, 4, 5]); T := array(1..5, [1, 3, 7, 15, 31]); a(5) := d(V)*evalm(S&*T);
CROSSREFS
Sequence in context: A202964 A352322 A183469 * A296392 A318011 A328685
KEYWORD
nonn,more
AUTHOR
S. Bujnowski (slawb(AT)atr.bydgoszcz.pl), Feb 13 2002
STATUS
approved

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Last modified April 22 00:17 EDT 2024. Contains 371886 sequences. (Running on oeis4.)