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A225686
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a(n) = Fibonacci(2*n^2), a "Somos-like" sequence.
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1
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1, 21, 2584, 2178309, 12586269025, 498454011879264, 135301852344706746049, 251728825683549488150424261, 3210056809456107725247980776292056, 280571172992510140037611932413038677189525
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listen;
history;
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OFFSET
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1,2
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LINKS
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FORMULA
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a(1) = 1, a(2) = 21, a(3) = 2584, a(4) = 2178309, a(5) = 12586269025, and for n>=6, a(n) = ( 2303a(n - 4)a(n - 3)a(n - 1) + 2255a(n - 3)^2 a(n - 2) + 329a(n - 4)a(n - 1)^2 - 15792a(n - 4)a(n - 2)^2 + 329a(n - 4)a(n - 3)^2 - 2303a(n - 4)^2 a(n - 2) + 441a(n - 2) - a(n-2)^3-2961a(n-4) - a(n-5)a(n-2)a(n-1) + 329a(n-5)a(n-3)a(n-2) )/( 48a(n-4)a(n-2) ).
0 = a(n)*(+233805165*a(n+4) - 726110*a(n+6)) + a(n+1)*(-76921899285*a(n+3) + 75284537349*a(n+7)) + a(n+2)*(+11222647920*a(n+2) + 3613692630240*a(n+4) - 1138829425306704*a(n+6) - 34837488*a(n+8)) + a(n+3)*(-527230649330*a(n+3) + 526991761443*a(n+7) + 329*a(n+9)) + a(n+4)*(+516007999155*a(n+4) - 1636636155*a(n+6) - 4976784*a(n+8)) + a(n+6)*(2255*a(n+6)). for all n in Z. - Michael Somos, Dec 05 2016
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MAPLE
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if n <= 5 then
op(n, [1, 21, 2584, 2178309, 12586269025]) ;
else
( 2303*procname(n - 4)*procname(n - 3)*procname(n - 1)
+ 2255*procname(n - 3)^2*procname(n - 2)
+ 329*procname(n - 4)*procname(n - 1)^2
- 15792*procname(n - 4)*procname(n - 2)^2
+ 329*procname(n - 4)*procname(n - 3)^2
- 2303*procname(n - 4)^2*procname(n - 2)
+ 441*procname(n - 2)
- procname(n-2)^3
-2961*procname(n-4)
- procname(n-5)*procname(n-2)*procname(n-1)
+ 329*procname(n-5)*procname(n-3)*procname(n-2) )
/ 48/procname(n-4)/procname(n-2) ;
end if;
# second Maple program:
a:= n-> (<<0|1>, <1|1>>^(2*n^2))[1, 2]:
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MATHEMATICA
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PROG
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(PARI) {a(n) = fibonacci(2 * n^2)}; /* Michael Somos, Dec 05 2016 */
(Magma) [Fibonacci(2*n^2): n in [1..10]]; // G. C. Greubel, Aug 09 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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