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A270444
Expansion of 2*(1+2*x) / (1-8*x+4*x^2).
1
2, 20, 152, 1136, 8480, 63296, 472448, 3526400, 26321408, 196465664, 1466439680, 10945654784, 81699479552, 609813217280, 4551707820032, 33974409691136, 253588446248960, 1892809931227136, 14128125664821248, 105453765593661440
OFFSET
1,1
COMMENTS
If p is an odd prime, a((p+1)/2) == 2 mod p. In other words, a((p+1)/2) - 2^p is divisible by p where p is an odd prime.
FORMULA
G.f.: 2*(1+2*x)/(1-8*x+4*x^2).
a(n) = (1+sqrt(3))^(2*n-1) + (1-sqrt(3))^(2*n-1).
a(n) = 2 * A107903(n-1).
EXAMPLE
a(2) = 20 because (1 + sqrt(3))^3 + (1 - sqrt(3))^3 = 20.
MATHEMATICA
CoefficientList[Series[2(1+2x)/(1-8x+4x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -4}, {2, 20}, 30] (* Harvey P. Dale, Jun 09 2020 *)
PROG
(PARI) Vec(2*(1+2*x)/(1-8*x+4*x^2) + O(x^100))
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 17 2016
STATUS
approved