A110293 a(2*n) = A001570(n), a(2*n+1) = A011943(n+1).

1, 7, 13, 97, 181, 1351, 2521, 18817, 35113, 262087, 489061, 3650401, 6811741, 50843527, 94875313, 708158977, 1321442641, 9863382151, 18405321661, 137379191137, 256353060613, 1913445293767, 3570537526921, 26650854921601, 49731172316281, 371198523608647

Offset

0,2

Comments

See also A110294 (compare program code).

a(2*n+1) = (a(2*n) + a(2*n+2))/2 and see A232765 for Diophantine equation that produces a sequence related to a(n). - Richard R. Forberg, Nov 30 2013

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1).

Formula

G.f.: (1+7*x-x^2-x^3) / ((1-4*x+x^2)*(1+4*x+x^2)).

From Colin Barker, Nov 01 2016: (Start)

a(n) = (3-(-1)^n)*((-3+2*sqrt(3))*(2-sqrt(3))^n + (3+2*sqrt(3))*(2+sqrt(3))^n )/(8*sqrt(3)).

a(n) = 14*a(n-2) - a(n-4) for n>3. (End)

a(n) = (1/4)*(3 - (-1)^n)*(2*A001353(n) - A001353(n-1)). - G. C. Greubel, Jan 04 2023

Maple

seriestolist(series((1+7*x-x^2-x^3)/((1-4*x+x^2)*(1+4*x+x^2)), x=0, 25));

Mathematica

CoefficientList[Series[(1+7x-x^2-x^3)/((1-4x+x^2)(1+4x+x^2)), {x, 0, 25}], x] (* Michael De Vlieger, Nov 01 2016 *)

Prog

(PARI) Vec((1+7*x-x^2-x^3)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 01 2016
(Magma)
A001353:= func< n | Evaluate(ChebyshevSecond(n+1), 2) >;
[(3-(-1)^n)*(2*A001353(n) - A001353(n-1))/4: n in [0..40]]; // G. C. Greubel, Jan 04 2023
(SageMath)
def A001353(n): return chebyshev_U(n, 2)
[(3-(-1)^n)*(2*A001353(n) - A001353(n-1))/4 for n in range(41)] # G. C. Greubel, Jan 04 2023

Crossrefs

Cf. A001353, A001570, A011943, A110294, A232765.

Sequence in context: A177952 A320461 A132373 * A253333 A039687 A001544

Adjacent sequences: A110290 A110291 A110292 * A110294 A110295 A110296

Keyword

easy,nonn

Author

Creighton Dement, Jul 18 2005

Status

approved