OFFSET
0,6
LINKS
W. C. Lynch, The t-Fibonacci numbers and polyphase sorting, Fib. Quart., 8 (1970), pp. 6ff.
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
Index entries for linear recurrences with constant coefficients, signature (3, 2, 3, 7, 14, -32, -2, 6, -4, -6, 10, 1, -1, 0, 1, -1).
FORMULA
a(n) = F_5(1)^2 + F_5(1)^2 + F_5(2)^2 + ... F_5(n)^2 where F_5(n) = A001591(n). a(0) = 0, a(n+1) = a(n) + A001591(n)^2.
a(n)= 3*a(n-1) +2*a(n-2) +3*a(n-3) +7*a(n-4) +14*a(n-5) -32*a(n-6) -2*a(n-7) +6*a(n-8) -4*a(n-9) -6*a(n-10) +10*a(n-11) +a(n-12) -a(n-13) +a(n-15) -a(n-16). [R. J. Mathar, Aug 11 2009]
G.f.: x^4*(x^10 +x^9 +x^7 +x^6 -6*x^5 -5*x^4 -3*x^3 -2*x^2 -x +1) / ((x -1)*(x^5 +x^4 +x^3 +3*x^2 +3*x -1)*(x^10 -x^9 -x^7 +x^6 -6*x^5 +3*x^4 +3*x^3 +2*x^2 +x +1)). - Colin Barker, May 08 2013
EXAMPLE
a(0) = 0 = 0^2 since F_5(0) = A001591(0) = 0.
a(1) = 0 = 0^2 + 0^2
a(2) = 0 = 0^2 + 0^2 + 0^2
a(3) = 0 = 0^2 + 0^2 + 0^2 + 0^2
a(4) = 1 = 0^2 + 0^2 + 0^2 + 0^2 + 1^2
a(5) = 2 = 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2
a(6) = 6 = 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2
a(7) = 22 = 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2
a(8) = 86 = 8^2 + 22
a(9) = 342 = 16^2 + 86
MATHEMATICA
Accumulate[LinearRecurrence[{1, 1, 1, 1, 1}, {0, 0, 0, 0, 1}, 30]^2] (* Harvey P. Dale, Jan 04 2015 *)
LinearRecurrence[{3, 2, 3, 7, 14, -32, -2, 6, -4, -6, 10, 1, -1, 0, 1, -1}, {0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1303, 5024, 19424, 75120, 290416, 1122160}, 28] (* Ray Chandler, Aug 02 2015 *)
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Jonathan Vos Post, May 19 2005
EXTENSIONS
a(26) and a(27) corrected by R. J. Mathar, Aug 11 2009
STATUS
approved