A094567 Associated with alternating row sums of array in A094566.
1, 4, 30, 203, 1394, 9552, 65473, 448756, 3075822, 21081995, 144498146, 990405024, 6788337025, 46527954148, 318907342014, 2185823439947, 14981856737618, 102687173723376, 703828359326017, 4824111341558740, 33064951031585166, 226630545879537419
Offset: 0
Examples
Obtain 4,30,203 from a(0)=1 and Fibonacci numbers 1,5,34,233: 4=5-1, 30=34-4, 203=233-30.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,6,-1).
Programs
-
Mathematica
RecurrenceTable[{a[0]==1,a[n]==Fibonacci[4n+1]-a[n-1]},a[n],{n,30}] (* or *) LinearRecurrence[{6,6,-1},{1,4,30},31] (* Harvey P. Dale, Jul 13 2011 *) -
PARI
Vec(-(2*x-1)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014
-
PARI
vector(30, n, n--; (fibonacci(4*n+3) + (-1)^n)/3) \\ Michel Marcus, Nov 19 2014
Formula
a(n) = F(4n+1) - a(n-1) for n >= 1, with a(0) = 1.
a(n) = (Fib(4n+3) + (-1)^n)/3. - Ralf Stephan, Dec 04 2004
a(n) = 6*a(n-1)+6*a(n-2)-a(n-3), with a(0)=1, a(1)=4, a(2)=30. - Harvey P. Dale, Jul 13 2011
G.f.: (1-2*x)/(1-6*x-6*x^2+x^3). - Harvey P. Dale, Jul 13 2011
a(n) = (-1)^n*sum((-1)^k*Fibonacci(4*k+1), k=0..n). - Gary Detlefs, Jan 22 2013
a(n) = (2^(-n)*(5*(-2)^n+(7-3*sqrt(5))^n*(5-2*sqrt(5))+(5+2*sqrt(5))*(7+3*sqrt(5))^n))/15. - Colin Barker, Mar 05 2016
Extensions
More terms from Harvey P. Dale, Jul 13 2011