A391054 a(n) = 9*n+1 if n is odd and (n + (n mod 4))/4 if n is even.

0, 10, 1, 28, 1, 46, 2, 64, 2, 82, 3, 100, 3, 118, 4, 136, 4, 154, 5, 172, 5, 190, 6, 208, 6, 226, 7, 244, 7, 262, 8, 280, 8, 298, 9, 316, 9, 334, 10, 352, 10, 370, 11, 388, 11, 406, 12, 424, 12, 442, 13, 460, 13, 478, 14, 496, 14, 514, 15, 532, 15, 550, 16, 568

Offset

0,2

Comments

Does iterating n -> a(n) always reach 1 (i.e., the cycle 1 -> 10 -> 3 -> 28 -> 7 -> 64 -> 16 -> 4 -> 1)?

Links

James C. McMahon, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Formula

a(4*n) = a(4*n-2) for n > 0.

a(2*n+1) = a(2*n-1) + 18 for n > 0.

a(n) = a(n-2) + a(n-4) - a(n-6).

G.f.: (10*x + x^2 + 18*x^3 + 8*x^5) / ((1 - x^2) * (1 - x^4)).

E.g.f.: (-cos(x) + (1 + 36*x)*cosh(x) + (4 + x)*sinh(x))/4. - Stefano Spezia, Nov 26 2025

Mathematica

a[n_] := If[OddQ[n], 9*n + 1, (n + Mod[n, 4])/4]; Array[a, 100, 0] (* Amiram Eldar, Nov 26 2025 *)

Prog

(PARI) a(n) = if(n%2 == 0, (n + n%4)/4, n*9+1)
(Python)
def A391054(n): return 9*n+1 if n&1 else n+(n&3)>>2 # Chai Wah Wu, Nov 28 2025

Crossrefs

Cf. A006370.

Sequence in context: A050999 A223450 A221311 * A361949 A070246 A085044

Adjacent sequences: A391051 A391052 A391053 * A391055 A391056 A391057

Keyword

nonn,easy

Author

Werner Schulte, Nov 26 2025

Status

approved