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A329005
a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
3
1, 1, 1, 5, 11, 7, 43, 85, 19, 341, 683, 455, 2731, 5461, 3641, 21845, 43691, 9709, 174763, 349525, 233017, 1398101, 2796203, 1864135, 11184811, 22369621, 1657009, 89478485, 178956971, 119304647, 715827883, 1431655765, 954437177, 5726623061, 11453246123
OFFSET
1,4
COMMENTS
a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
EXAMPLE
See Example in A327320.
MATHEMATICA
c[poly_] := If[Head[poly] === Times, Times @@ DeleteCases[(#1 (Boole[MemberQ[#1, x] || MemberQ[#1, y] || MemberQ[#1, z]] &) /@Variables /@ #1 &)[List @@ poly], 0], poly];
r = Sqrt[2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]]; (* A327320 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329005 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329006 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329007 *)
(* Peter J. C. Moses, Nov 01 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Nov 08 2019
STATUS
approved