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A168314
Eigensequence of triangle A168313.
2
1, 1, 3, 5, 13, 29, 71, 165, 401, 957, 2315, 5561, 13437, 32377, 78191, 188617, 455425, 1099137, 2653699, 6405733, 15465165, 37334149, 90133463, 217596445, 525326353, 1268238029, 3061802411, 7391815977, 17845434365, 43082619953, 104010674271, 251103812113
OFFSET
1,3
COMMENTS
Conjectured convergent of a(n)/a(n-1) = (1+sqrt(2)). E.g.: a(19)/a(18) = 2653699/1099137 = 2.4143478...
FORMULA
Equals the eigensequence of triangle A168313 = lim_{n->oo} M^n where M = A168313 shifted down one row and inserting a "1" at top.
Equals the left column vector as a sequence.
PROG
(Python)
a = [1]
for n in range(30):
a.append(2*sum(a[n//2:-1]) + a[-1])
print(a) # Andrey Zabolotskiy, Aug 28 2024
CROSSREFS
Sequence in context: A238216 A067932 A339155 * A335562 A106666 A124791
KEYWORD
eigen,nonn
AUTHOR
Gary W. Adamson, Nov 22 2009
EXTENSIONS
Terms a(20) and beyond from Andrey Zabolotskiy, Aug 28 2024
STATUS
approved