login
A331211
Number of green nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and one green node.
2
1, 15, 117, 891, 6777, 51543, 392013, 2981475, 22675761, 172461663, 1311666021, 9975943179, 75872547369, 577052549415, 4388802753213, 33379264377459, 253867706760033, 1930803860947887, 14684827767302997, 111686210555580315, 849435201142733529, 6460422977475127287
OFFSET
0,2
LINKS
FORMULA
a(n) = a(n-1) + 2*b(n-1), b(n) = 2*a(n-1) + 7*b(n-1) with a(0) = 1 and b(0) = 7 where b(n) = A332936(n).
From Colin Barker, Mar 03 2020: (Start)
G.f.: (1 + 7*x) / (1 - 8*x + 3*x^2).
a(n) = 8*a(n-1) - 3*a(n-2) for n>1.
(End)
From Stefano Spezia, Mar 03 2020: (Start)
a(n) = ((4 - sqrt(13))^n*(-11 + sqrt(13)) + (4 + sqrt(13))^n*(11 + sqrt(13)))/(2*sqrt(13)).
E.g.f.: exp(4*x)*cosh(sqrt(13)*x) + (11*exp(4*x)*sinh(sqrt(13)*x))/sqrt(13).
(End)
EXAMPLE
For n = 2 take g(1)=15 and b(1)=51. Multiply b(1) by 2 to get 102 add 15 to get 117.
For n = 3 take g(2)=117 and b(2)=387. Multiply b(2) by 2 to get 774 add 177 to get 891.
PROG
(Python)
g=1
b=7
sg=0
sb=0
bl=[]
gl=[]
for int in range(1, 20):
sg=g*1+b*2
sb=b*7+g*2
g=sg
b=sb
gl.append(g)
bl.append(b)
print(gl)
(PARI) Vec((1 + 7*x) / (1 - 8*x + 3*x^2) + O(x^20)) \\ Colin Barker, Mar 03 2020
CROSSREFS
Cf. A332936 (number of blue nodes).
Similar sequences with a cycle size 3..6 are: A007483, A048876, A189274(n+1), A054490.
Sequence in context: A125352 A126510 A328725 * A183475 A253804 A161476
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(14)-a(21) from Stefano Spezia, Mar 03 2020
Typo in a(14) fixed by Colin Barker, Apr 26 2020
STATUS
approved