A099462 Expansion of x/(1 - 4*x^2 - 4*x^3).

0, 1, 0, 4, 4, 16, 32, 80, 192, 448, 1088, 2560, 6144, 14592, 34816, 82944, 197632, 471040, 1122304, 2674688, 6373376, 15187968, 36192256, 86245376, 205520896, 489750528, 1167065088, 2781085696, 6627262464, 15792603136, 37633392640

Offset

0,4

Comments

Binomial transform is A099463.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,4).

Formula

a(n) = 4*a(n-2) + 4*a(n-3).

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(k, n-2*k-1)*4^k.

a(n+1) = Sum_{k=0..floor(n/2)} C((n-k)/2, k)*(1+(-1)^(n-k))*2^(n-k). - Paul Barry, Sep 09 2005

Mathematica

LinearRecurrence[{0, 4, 4}, {0, 1, 0}, 40] (* G. C. Greubel, Nov 18 2021 *)

Prog

(Magma) [n le 3 select (1+(-1)^n)/2 else 4*(Self(n-2) +Self(n-3)): n in [1..41]]; // G. C. Greubel, Nov 18 2021
(Sage)
def a(n): return sum( 4^k*binomial(k, n-2*k-1) for k in (0..(n-1)//2) )
[a(n) for n in (0..40)] # G. C. Greubel, Nov 18 2021

Crossrefs

Cf. A099463.

Sequence in context: A322039 A158101 A038234 * A218051 A092266 A257606

Adjacent sequences: A099459 A099460 A099461 * A099463 A099464 A099465

Keyword

easy,nonn

Author

Paul Barry, Oct 16 2004

Status

approved