login
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
OFFSET
0,1
COMMENTS
a(n) = A078057(n) + 1 (see A288213). - Michel Dekking, Sep 29 2019
LINKS
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 23 2012
STATUS
approved