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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 16 2004
STATUS
approved