A299914 a(n) = a(n-1) + 3*a(n-2) if n even, or 2*a(n-1) + 4*a(n-2) if n odd, starting with 0, 1.

0, 1, 1, 6, 9, 42, 69, 306, 513, 2250, 3789, 16578, 27945, 122202, 206037, 900882, 1518993, 6641514, 11198493, 48963042, 82558521, 360969210, 608644773, 2661166386, 4487100705, 19618866954, 33080169069, 144635805954, 243876313161, 1066295850138, 1797924789621

Offset

0,4

References

Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,9,0,-12)

Formula

G.f.: -x*(3*x^2-x-1)/(12*x^4-9*x^2+1). - Alois P. Heinz, Mar 10 2018

a(n) = 9*a(n-2) - 12*a(n-4) for n>3. - Colin Barker, Mar 11 2018

Maple

a:= n-> (<<0|1>, <-12|9>>^iquo(n, 2, 'r'). <<r, 5*r+1>>)[1, 1]:
seq(a(n), n=0..35);  # Alois P. Heinz, Mar 10 2018

Mathematica

Fold[Append[#1, Inner[Times, Boole[OddQ@ #2] + {1, 3}, {#1[[-1]], #1[[-2]]}, Plus]] &, {0, 1}, Range[2, 30]] (* or *)
CoefficientList[Series[-x (3 x^2 - x - 1)/(12 x^4 - 9 x^2 + 1), {x, 0, 30}], x] (* Michael De Vlieger, Mar 10 2018 *)

Prog

(PARI) concat(0, Vec(x*(1 + x - 3*x^2) / (1 - 9*x^2 + 12*x^4) + O(x^30))) \\ Colin Barker, Mar 11 2018

Crossrefs

Bisections give A299915, A299916.

Cf. A299913.

Sequence in context: A147355 A154139 A330983 * A187998 A177181 A126110

Adjacent sequences: A299911 A299912 A299913 * A299915 A299916 A299917

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 10 2018

Extensions

More terms from Altug Alkan, Mar 10 2018

Status

approved