A114954 A 3/2-power Fibonacci sequence.

1, 1, 2, 4, 11, 45, 339, 6544, 535619, 392527477, 7777266564708, 21689055127418446258, 101009204076980364695686091211

Offset

0,3

Comments

This sequence is related to: A112961 "a cubic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^3 + a(n-2)^3 A112969 "a quartic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^4 + a(n-2)^4, which is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. Primes in this sequence include a(n) for n = 2, 4. Semiprimes in this sequence include a(n) for n = 3, 6.

Links

Table of n, a(n) for n=0..12.

Formula

a(0) = a(1) = 1, for n>1 a(n) = ceiling(a(n-1)^(3/2) + a(n-2)^(3/2)).

Example

a(2) = ceiling(a(0)^(3/2) + a(1)^(3/2)) = ceiling(1^1.5 + 1^1.5) = 2.
a(3) = ceiling(a(1)^(3/2) + a(2)^(3/2)) = ceiling(1^1.5 + 2^1.5) = ceiling(3.82842712) = 4.
a(4) = ceiling(2^(3/2) + 4^(3/2)) = ceiling(10.8284271) = 11.
a(5) = ceiling((4^(3/2)) + (11^(3/2))) = ceiling(44.4828727) = 45.
a(6) = ceiling((11^(3/2)) + (45^(3/2))) = ceiling(338.35205) = 339.
a(7) = ceiling((45^(3/2)) + (339^(3/2))) = ceiling(6543.52112) = 6544.

Mathematica

RecurrenceTable[{a[0]==a[1]==1, a[n]==Ceiling[Surd[ a[n-1]^3, 2]+ Surd[ a[n-2]^3, 2]]}, a, {n, 15}] (* Harvey P. Dale, Apr 07 2016 *)

Crossrefs

Cf. A000283, A112961, A112969, A114793.

Sequence in context: A328437 A107703 A140838 * A134019 A120259 A174632

Adjacent sequences: A114951 A114952 A114953 * A114955 A114956 A114957

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 21 2006

Status

approved