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.

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.

Links

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

Index entries for linear recurrences with constant coefficients, signature (-1,8,8)

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.

Cf. A299914, A299915, A299916.

Sequence in context: A258183 A038275 A261669 * A226197 A356779 A263836

Adjacent sequences: A299910 A299911 A299912 * A299914 A299915 A299916

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 10 2018

Extensions

More terms from Altug Alkan, Mar 10 2018

Status

approved