A160079 Lodumo_3 of Fibonacci numbers.

0, 1, 4, 2, 3, 5, 8, 7, 6, 10, 13, 11, 9, 14, 17, 16, 12, 19, 22, 20, 15, 23, 26, 25, 18, 28, 31, 29, 21, 32, 35, 34, 24, 37, 40, 38, 27, 41, 44, 43, 30, 46, 49, 47, 33, 50, 53, 52, 36, 55, 58, 56, 39, 59, 62, 61, 42, 64, 67, 65, 45, 68, 71, 70, 48, 73, 76, 74, 51, 77, 80, 79, 54

Offset: 0

Author

Philippe Deléham, May 01 2009

Keywords

• nonn
• easy

Comments

Permutation of nonnegative integers.

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 (0,0,0,1,0,0,0,1,0,0,0,-1).

Crossrefs

Cf. A000045, A082115, A160016, A160051, A367651 (inverse permutation).

Formula

a(n) = lod_3(A000045(n)).

a(n) = 2*a(n-8) - a(n-16) for n >= 16. - Philippe Deléham, Mar 09 2023

a(8*n) = 6*n, a(8*n+1) = 9*n+1, a(8*n+2) = 9*n+4, a(8*n+3) = 9*n+2, a(8*n+4) = 6*n+3, a(8*n+5) = 9*n+5, a(8*n+6) = 9*n+8, a(8*n+7) = 9*n+7. - Philippe Deléham, Nov 24 2023

From Philippe Deléham, Nov 29 2023 : (Start)

a(n) = a(n-4) + a(n-8) - a(n-12) for n >= 12.

G.f. : (x + 4*x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 4*x^6 + 5*x^7 + 3*x^8 + 4*x^9 + x^10 + 2*x^11) / (1 - x^4 - x^8 + x^12). (End)