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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8, -4).

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

Cf. A077444, A080040, A080041, A107903.

Sequence in context: A105489 A093302 A248337 * A093130 A043029 A164944

Adjacent sequences:  A270441 A270442 A270443 * A270445 A270446 A270447

KEYWORD

nonn

AUTHOR

Altug Alkan, Mar 17 2016

STATUS

approved

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Last modified August 5 08:27 EDT 2021. Contains 346464 sequences. (Running on oeis4.)