OFFSET
0,2
COMMENTS
M has 2 parents, 4 grandparents, and so on up to 2^n ancestors at the top of the tree.
The genetic relatives of M are all descendants of the ancestors.
M is a genetic relative of himself or herself.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-26,16).
FORMULA
a(n) = 2^n + 4*(8^n - 1)/7.
From Stefano Spezia, Nov 25 2022: (Start)
O.g.f.: (1 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 8*x)).
E.g.f.: exp(x)*(4*(exp(7*x) - 1) + 7*exp(x))/7.
a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3) for n > 2. (End)
MATHEMATICA
LinearRecurrence[{11, -26, 16}, {1, 6, 40}, 25] (* Paolo Xausa, Feb 09 2024 *)
PROG
(Python) for n in range(0, 10): print(2**n+4*(8**n-1)//7)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Hans Braxmeier, Nov 19 2022
STATUS
approved