A027006 a(n) = T(2*n+1, n+3), T given by A026998.

1, 34, 281, 1397, 5353, 17643, 53062, 150833, 414210, 1114160, 2960806, 7814074, 20544191, 53902532, 141273663, 370060623, 969088727, 2537431693, 6643486220, 17393369595, 45537037936, 119218243314, 312118286876, 817137321092, 2139294503373, 5600747154678

Offset

2,2

Comments

Bisection of A053298.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (8,-26,45,-45,26,-8,1).

Formula

G.f.: x^2*(1+26*x+35*x^2-12*x^3-2*x^4) / ((1-x)^5*(1-3*x+x^2)). - Colin Barker, Feb 19 2016

From G. C. Greubel, Jul 22 2025: (Start)

a(n) = Lucas(2*n+7) - (12*n^4 + 20*n^3 + 81*n^2 + 169*n + 174)/6.

E.g.f.: exp(3*x/2)*(29*cosh(p*x) + 26*p*sinh(p*x)) - (1/6)*(174 + 282*x + 225*x^2 + 92*x^3 + 12*x^4)*exp(x), where 2*p = sqrt(5). (End)

Mathematica

A027006[n_]:= LucasL[2*n+7] -(12*n^4 +20*n^3 +81*n^2 +169*n +174)/6;
Table[A027006[n], {n, 2, 42}] (* G. C. Greubel, Jul 22 2025 *)

Prog

(PARI) Vec(x^2*(1+26*x+35*x^2-12*x^3-2*x^4) / ((1-x)^5*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 19 2016
(Magma)
A027006:= func< n | Lucas(2*n+7) -(12*n^4 +20*n^3 +81*n^2 +169*n +174)/6 >;
[A027006(n): n in [2..40]]; // G. C. Greubel, Jul 22 2025
(SageMath)
def A027006(n): return lucas_number2(2*n+7, 1, -1) -(12*n^4 +20*n^3 +81*n^2 +169*n +174)//6
print([A027006(n) for n in range(2, 41)]) # G. C. Greubel, Jul 22 2025

Crossrefs

Cf. A000032, A026998, A053298.

Sequence in context: A252999 A229327 A209891 * A156531 A220565 A230803

Adjacent sequences: A027003 A027004 A027005 * A027007 A027008 A027009

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved