A054320 -id:A054320 - cp's OEIS frontend

A152448 a(0)=a(1)=1, a(2)=6, a(3)=11; a(n+4) = 10*a(n+2) - a(n).

1, 1, 6, 11, 59, 109, 584, 1079, 5781, 10681, 57226, 105731, 566479, 1046629, 5607564, 10360559, 55509161, 102558961, 549484046, 1015229051, 5439331299, 10049731549, 53843828944, 99482086439, 532998958141, 984771132841, 5276145752466, 9748229241971, 52228458566519

Offset: 0

Richard Choulet, Dec 04 2008

Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

Cf. A054320 (bisection).

LinearRecurrence[{0,10,0,-1},{1,1,6,11},30] (* Harvey P. Dale, Nov 10 2018 *)

a(n) = ((1/48)*sqrt(3)*sqrt(2) + 1/4 + (1/8)*sqrt(2))*(sqrt(3) + sqrt(2))^n + (-(1/48)*sqrt(3)*sqrt(2) + 1/4 - (1/8)*sqrt(2))*(sqrt(3) - sqrt(2))^n + ((1/48)*sqrt(3)*sqrt(2) + 1/4 - (1/8)*sqrt(2))*(-sqrt(3) - sqrt(2))^n + (1/4 - (1/48)*sqrt(3)*sqrt(2) + (1/8)*sqrt(2))*(-sqrt(3) + sqrt(2))^n.
From R. J. Mathar and Philippe Deléham, Dec 05 2008: (Start)
a(2n) = A004189(n+1) - 4*A004189(n).
a(2n+1) = A004189(n) + A004189(n+1).
G.f.: (1+x-4x^2+x^3) / (1-10x^2+x^4). (End)

A350965 a(n) = sqrt(6*A138288(n)^2 - 2).

Original entry on oeis.org

2, 22, 218, 2158, 21362, 211462, 2093258, 20721118, 205117922, 2030458102, 20099463098, 198964172878, 1969542265682, 19496458483942, 192995042573738, 1910453967253438, 18911544629960642, 187204992332352982, 1853138378693569178

Offset: 0

N. J. A. Sloane, Mar 02 2022

H. Brocard, Note #2049, L'Intermédiaire des Mathématiciens, 8 (1901), pp. 212-213.

Index entries for linear recurrences with constant coefficients, signature (10,-1).

Cf. A138288. Equals 2*A054320.

G.f.: 2*(1+x)/(1-10*x+x^2) . - R. J. Mathar, Mar 07 2022

cp's OEIS Frontend

A152448 a(0)=a(1)=1, a(2)=6, a(3)=11; a(n+4) = 10*a(n+2) - a(n).

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