A147666 List of triples (0, 6n+1, 6n+5) for n = 0, 1, 2, ...

0, 1, 5, 0, 7, 11, 0, 13, 17, 0, 19, 23, 0, 25, 29, 0, 31, 35, 0, 37, 41, 0, 43, 47, 0, 49, 53, 0, 55, 59, 0, 61, 65, 0, 67, 71, 0, 73, 77, 0, 79, 83, 0, 85, 89, 0, 91, 95, 0, 97, 101, 0, 103, 107, 0, 109, 113, 0, 115, 119, 0, 121, 125, 0, 127, 131, 0, 133, 137, 0, 139, 143, 0, 145, 149

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

G.f.: x*(1 + 5*x + 5*x^3 + x^4)/(1 - x^3)^2. - Georg Fischer, Dec 03 2024

a(n) = 4*n/3 + (6*A049347(n) - A049347(n-1))/3 - 2*(-1)^n*(A099254(n) - A099254(n-1)). - G. C. Greubel, Dec 09 2025

Example

Terms begin:
  0,  1,  5;
  0,  7, 11;
  0, 13, 17;
  0, 19, 23;
  ...

Mathematica

LinearRecurrence[{0, 0, 2, 0, 0, -1}, {0, 1, 5, 0, 7, 11}, 100] (* Georg Fischer, Dec 03 2024 *)

Prog

(Magma)
I:= [0, 1, 5, 0, 7, 11]; [n le 6 select I[n] else 2*Self(n-3) -Self(n-6): n in [1..100]]; // G. C. Greubel, Dec 09 2025
(SageMath)
@CachedFunction
def A147666(n):
    if n<6: return (0, 1, 5, 0, 7, 11)[n]
    else: return 2*A147666(n-3) -A147666(n-6)
[A147666(n) for n in range(101)] # G. C. Greubel, Dec 09 2025

Crossrefs

Cf. A049347, A099254.

Trisections give: A000004, A016921, A016969.

Sequence in context: A244045 A084248 A201417 * A380283 A343071 A215892

Adjacent sequences: A147663 A147664 A147665 * A147667 A147668 A147669

Keyword

nonn,tabf,easy

Author

Milton L. Brown (miltbrown(AT)earthlink.net), Nov 10 2008

Extensions

More terms from Robert G. Wilson v, Dec 07 2008

Edited by N. J. A. Sloane, Dec 07 2008

Status

approved