This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114954 #9 Apr 07 2016 18:23:57
%S A114954 1,1,2,4,11,45,339,6544,535619,392527477,7777266564708,
%T A114954 21689055127418446258,101009204076980364695686091211
%N A114954 A 3/2-power Fibonacci sequence.
%C A114954 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.
%F A114954 a(0) = a(1) = 1, for n>1 a(n) = ceiling(a(n-1)^(3/2) + a(n-2)^(3/2)).
%e A114954 a(2) = ceiling(a(0)^(3/2) + a(1)^(3/2)) = ceiling(1^1.5 + 1^1.5) = 2.
%e A114954 a(3) = ceiling(a(1)^(3/2) + a(2)^(3/2)) = ceiling(1^1.5 + 2^1.5) = ceiling(3.82842712) = 4.
%e A114954 a(4) = ceiling(2^(3/2) + 4^(3/2)) = ceiling(10.8284271) = 11.
%e A114954 a(5) = ceiling((4^(3/2)) + (11^(3/2))) = ceiling(44.4828727) = 45.
%e A114954 a(6) = ceiling((11^(3/2)) + (45^(3/2))) = ceiling(338.35205) = 339.
%e A114954 a(7) = ceiling((45^(3/2)) + (339^(3/2))) = ceiling(6543.52112) = 6544.
%t A114954 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 *)
%Y A114954 Cf. A000283, A112961, A112969, A114793.
%K A114954 easy,nonn
%O A114954 0,3
%A A114954 _Jonathan Vos Post_, Feb 21 2006