A182780 Twice A024537.

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

Offset

0,1

Comments

a(n) = A078057(n) + 1 (see A288213). - Michel Dekking, Sep 29 2019

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
(Magma) a:=[2, 4, 8]; [n le 3 select a[n] else 3*Self(n-1) - Self(n-2) - Self(n-3):n in [1..35]]; // Marius A. Burtea, Sep 29 2019

Crossrefs

Cf. A024537.

Sequence in context: A306200 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