A168314 Eigensequence of triangle A168313.

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...

Links

Table of n, a(n) for n=1..32.

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

Cf. A168313, A168315.

Sequence in context: A238216 A067932 A339155 * A335562 A106666 A124791

Adjacent sequences: A168311 A168312 A168313 * A168315 A168316 A168317

Keyword

eigen,nonn

Author

Gary W. Adamson, Nov 22 2009

Extensions

Terms a(20) and beyond from Andrey Zabolotskiy, Aug 28 2024

Status

approved