A094569 Associated with alternating row sums of array in A094568.
2, 11, 78, 532, 3649, 25008, 171410, 1174859, 8052606, 55193380, 378301057, 2592914016, 17772097058, 121811765387, 834910260654, 5722560059188, 39223010153665, 268838511016464, 1842646566961586, 12629687457714635, 86565165637040862, 593326472001571396
Offset: 0
Examples
Obtain 11,78,532 from a(0)=2 and Fibonacci numbers 13,89,610: 11=13-2, 78=89-11, 532=610-78.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly, 42:1 (2004), pp. 28-35.
- Index entries for linear recurrences with constant coefficients, signature (6,6,-1).
Programs
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Mathematica
LinearRecurrence[{6,6,-1},{2,11,78},30] (* Harvey P. Dale, Feb 15 2025 *) -
PARI
Vec(-(x-2)/((x+1)*(x^2-7*x+1)) + O(x^100)) \\ Colin Barker, Nov 19 2014
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PARI
vector(30, n, n--;(fibonacci(4*n+5) + (-1)^n)/3) \\ Michel Marcus, Nov 19 2014
Formula
a(n) = F(4n+3) - a(n-1) for n >= 1, where a(0) = 2.
a(n) = (Fib(4n+5) + (-1)^n )/3. - Ralf Stephan, Dec 04 2004
a(n) = (-1)^n * sum((-1)^k*Fibonacci(4*k+3), k=0..n). - Gary Detlefs, Jan 22 2013
a(n) = 6*a(n-1) + 6*a(n-2) - a(n-3). - Colin Barker, Nov 19 2014
G.f.: -(x-2) / ((x+1)*(x^2-7*x+1)). - Colin Barker, Nov 19 2014
Extensions
More terms from Colin Barker, Nov 19 2014