A080043 a(n)=floor((2+sqrt(7))^n).

1, 4, 21, 100, 465, 2164, 10053, 46708, 216993, 1008100, 4683381, 21757828, 101081457, 469599316, 2181641637, 10135364500, 47086382913, 218751625156, 1016265649365, 4721317472932, 21934066839825, 101900219778100

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (4, 4, -4, -3).

Programs

Mathematica

CoefficientList[Series[(1+t^2+4t^3)/(1-4t-4t^2+4t^3+3t^4), {t, 0, 25}], t]
With[{c=2+Sqrt[7]},Floor[c^Range[0,30]]] (* or *) LinearRecurrence[{4,4,-4,-3},{1,4,21,100},30]

Formula

G.f.: g(t)=(1+t^2+4t^3)/(1-4t-4t^2+4t^3+3t^4) a(n)=A080042(n)-(1+(-1)^n)/2

a(0)=1, a(1)=4, a(2)=21, a(3)=100, a(n)=4*a(n-1)+4*a(n-2)- 4*a(n-3)- 3*a(n-4). - Harvey P. Dale, Aug 11 2015