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A299913
a(n) = a(n-1) + 2*a(n-2) if n even, or 3*a(n-1) + 4*a(n-2) if n odd, starting with 0, 1.
2
0, 1, 1, 7, 9, 55, 73, 439, 585, 3511, 4681, 28087, 37449, 224695, 299593, 1797559, 2396745, 14380471, 19173961, 115043767, 153391689, 920350135, 1227133513, 7362801079, 9817068105, 58902408631, 78536544841, 471219269047, 628292358729, 3769754152375, 5026338869833
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*(2*x+1)/((x+1)*(8*x^2-1)). - Alois P. Heinz, Mar 10 2018
From Colin Barker, Mar 11 2018: (Start)
a(n) = (2^(3*n/2) - 1) / 7 for n even.
a(n) = 3*2^((3*(n-1))/2+1)/7 + 1/7 for n odd.
a(n) = -a(n-1) + 8*a(n-2) + 8*a(n-3) for n>2.
(End)
MAPLE
a:= n-> (<<0|1|0>, <0|0|1>, <8|8|-1>>^n. <<0, 1, 1>>)[1, 1]:
seq(a(n), n=0..35); # Alois P. Heinz, Mar 10 2018
MATHEMATICA
Fold[Append[#1, Inner[Times, 2 Boole[OddQ@ #2] + {1, 2}, {#1[[-1]], #1[[-2]]}, Plus]] &, {0, 1}, Range[2, 30]] (* or *)
CoefficientList[Series[-x (2 x + 1)/((x + 1) (8 x^2 - 1)), {x, 0, 30}], x] (* Michael De Vlieger, Mar 10 2018 *)
PROG
(PARI) concat(0, Vec(x*(1 + 2*x) / ((1 + x)*(1 - 8*x^2)) + O(x^40))) \\ Colin Barker, Mar 11 2018
CROSSREFS
Bisections give A023001, A083068.
Sequence in context: A258183 A038275 A261669 * A226197 A356779 A263836
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 10 2018
EXTENSIONS
More terms from Altug Alkan, Mar 10 2018
STATUS
approved