A259547 a(n) = n^4*Fibonacci(n).
0, 1, 16, 162, 768, 3125, 10368, 31213, 86016, 223074, 550000, 1303049, 2985984, 6654713, 14482832, 30881250, 64684032, 133383037, 271257984, 544872101, 1082400000, 2128789026, 4148908016, 8019403537, 15383789568, 29306640625, 55473687568, 104384578338
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-5,-10,15,11,-15,-10,5,5,1).
Programs
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Maple
a:= n-> n^4*(<<1|1>, <1|0>>^n)[1, 2]: seq(a(n), n=0..50); # Alois P. Heinz, Jun 30 2015
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Mathematica
Table[n^4 Fibonacci[n],{n,0,30}] (* or *) LinearRecurrence[{5,-5,-10,15,11,-15,-10,5,5,1},{0,1,16,162,768,3125,10368,31213,86016,223074},30] (* Harvey P. Dale, Mar 09 2016 *) -
PARI
a(n) = n^4*fibonacci(n)
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PARI
concat(0, Vec(-x*(x^8 -11*x^7 +87*x^6 -48*x^5 +240*x^4 +48*x^3 +87*x^2 +11*x +1)/(x^2 +x -1)^5 + O(x^50)))
Formula
G.f.: -x*(x^8-11*x^7+87*x^6-48*x^5+240*x^4+48*x^3+87*x^2+11*x+1) / (x^2+x-1)^5.
E.g.f.: exp(x/2)*x*(5*(1 + 7*x + 12*x^2 + 3*x^3)*cosh(sqrt(5)*x/2) + sqrt(5)*(1 + 21*x + 24*x^2 + 7*x^3)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Aug 25 2024