A240525 a(n) = 2^(n-2)*(2^(n+4)-(-1)^n+5).

5, 19, 68, 268, 1040, 4144, 16448, 65728, 262400, 1049344, 4195328, 16780288, 67112960, 268447744, 1073758208, 4295016448, 17179934720, 68719673344, 274878169088, 1099512414208, 4398047559680, 17592189190144, 70368748371968, 281474989293568, 1125899923619840

Offset: 0

Author

Vincenzo Librandi, Apr 07 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (4,4,-16).

Crossrefs

Cf. A000302, A084221.

Programs

Magma

[2^(n-2)*(2^(n+4)-(-1)^n+5): n in [0..25]];

Magma

I:=[5,19,68]; [n le 3 select I[n] else 4*Self(n-1)+4*Self(n-2)-16*Self(n-3): n in [1..30]];

Mathematica

CoefficientList[Series[(5 - x - 28 x^2)/(1 - 4 x - 4 x^2 + 16 x^3), {x, 0, 33}], x]

PARI

a(n)=(2^(n+4)-(-1)^n+5)<<(n-2) \\ Charles R Greathouse IV, Aug 26 2014

Formula

G.f.: (5-x-28*x^2)/(1-4*x-4*x^2+16*x^3).

a(n) = 4*a(n-1) + 4*a(n-2)- 16*a(n-3) with n>2, a(0)=5, a(1)=19, a(2)=68.

a(n) = (5*2^n-(-2)^n)/4+4^(n+1) = A084221(n)+A000302(n+1).