Alexa[x_]:=x^10+ x^9 + 2x^8 + 3x^7 + 5x^6 + 8x^5 + 8x^4 + 5x^3 + 3x^2 + 2x + 1

Alexa[1]

Alexa[2]

Alexa[3]

Alexa[1]

Alexa[100]

Class[x_]:=1+2x+3x^2+5x^3+8x^4+8x^5+5x^6+3x^7+2x^8+x^9+x^10

Class[x]

Alexa[x]

phi=(1+Sqrt[5])/2

phi^2

Expand[phi^2]

psi=(1-Sqrt[5])/2

Expand[psi^2]

F[n_]:=5^(-1/2) phi^n -5^(-1/2)psi^n

F[1]

Table[F[n],{n,1,10}]

Simplify[Table[F[n],{n,1,10}]]

Simplify[F[n]]

MP[x_]:=(1)+(-2)x+(14)x(x-1)/2+(12)x(x-1)(x-2)/6

Expand[MP[x]]

Table[MP[x],{x,0,7}]