A160080 Lodumo_4 of Fibonacci numbers.

0, 1, 5, 2, 3, 9, 4, 13, 17, 6, 7, 21, 8, 25, 29, 10, 11, 33, 12, 37, 41, 14, 15, 45, 16, 49, 53, 18, 19, 57, 20, 61, 65, 22, 23, 69, 24, 73, 77, 26, 27, 81, 28, 85, 89, 30, 31, 93, 32, 97, 101, 34, 35, 105, 36, 109, 113, 38, 39, 117, 40, 121, 125, 42, 43, 129, 44, 133, 137, 46

Offset: 0

Author

Philippe Deléham, May 01 2009

Keywords

• easy
• nonn

Comments

Permutation of nonnegative numbers.

Links

• OEIS wiki, Lodumo transform
• Index entries for sequences that are permutations of the nonnegative integers
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2,0,0,0,0,0,-1).

Crossrefs

Cf. A004767, A008586, A016825, A017533, A017581, A017629, A079343.

Formula

a(n) = lod_4(A000045(n)).

From Philippe Deléham, Nov 30 2023: (Start)

a(n) = 2*a(n-6) - a(n-12) for n >= 12.

a(6*n) = 4*n, a(6*n+1) = 12*n+1, a(6*n+2) = 12*n+5, a(6*n+3) = 4*n+2, a(6*n+4) = 4*n+3, a(6*n+5) = 12*n+9.

G.f.: (x + 5*x^2 + 2*x^3 + 3*x^4 + 9*x^5 + 4*x^6 + 11*x^7 + 7*x^8 + 2*x^9 + x^10 + 3*x^11) / ((1-x)^2*(1+x+x^2)^2*(1+x^3)^2). (End)