login
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.
4
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 10 2018
EXTENSIONS
More terms from Altug Alkan, Mar 10 2018
STATUS
approved