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A182780 Twice A024537. 4
2, 4, 8, 18, 42, 100, 240, 578, 1394, 3364, 8120, 19602, 47322, 114244, 275808, 665858, 1607522, 3880900, 9369320, 22619538, 54608394, 131836324, 318281040, 768398402, 1855077842, 4478554084, 10812186008, 26102926098, 63018038202, 152139002500, 367296043200, 886731088898, 2140758220994, 5168247530884 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

J. V. Leyendekkers and A. G. Shannon, Pellian sequence relationships among pi, e, sqrt(2), Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 58-62. See Table 2.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).

FORMULA

From Colin Barker, May 26 2018: (Start)

G.f.: 2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)).

a(n) = (2 + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.

a(n) = 3*a(n-1) - a(n-2) - a(n-3) for n>2.

(End)

PROG

(PARI) Vec(2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)) + O(x^40)) \\ Colin Barker, May 26 2018

CROSSREFS

Cf. A024537.

Sequence in context: A151381 A057151 A026699 * A078678 A261492 A027056

Adjacent sequences:  A182777 A182778 A182779 * A182781 A182782 A182783

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 23 2012

STATUS

approved

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Last modified November 14 15:07 EST 2018. Contains 317208 sequences. (Running on oeis4.)