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A270445
Expansion of 2*x*(1+4*x) / (1-12*x+16*x^2).
1
2, 32, 352, 3712, 38912, 407552, 4268032, 44695552, 468058112, 4901568512, 51329892352, 537533612032, 5629125066752, 58948963008512, 617321555034112, 6464675252273152, 67698958146732032, 708952693724413952, 7424248994345254912
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
a(n) = 12*a(n-1) - 16*a(n-2) for n>2. G.f.: 2*x*(1+4*x) / (1-12*x+16*x^2). - Colin Barker, Mar 17 2016
a(n) = (1+sqrt(5))^(2*n-1) + (1-sqrt(5))^(2*n-1).
EXAMPLE
a(2) = 32 because (1 + sqrt(5))^3 + (1 - sqrt(5))^3 = 32.
PROG
(PARI) Vec(2*x*(1+4*x)/(1-12*x+16*x^2) + O(x^50)) \\ Colin Barker, Mar 17 2016
CROSSREFS
Sequence in context: A323639 A060868 A350138 * A199019 A127697 A191467
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Mar 17 2016
STATUS
approved