A027018 a(n) = T(2*n+1, n+3), T given by A027011.

1, 9, 150, 1085, 5283, 20495, 69007, 212020, 613633, 1708508, 4640978, 12414802, 32903418, 86731043, 227905816, 597838223, 1566763325, 4103989113, 10747219441, 28140274566, 73676929931, 192894712070, 505012447636, 1322149114676, 3461442847524, 9062189100301

Offset

2,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-34,71,-90,71,-34,9,-1).

Formula

G.f.: x^2*(1+103*x^2-30*x^3+69*x^4-73*x^5+34*x^6-9*x^7+x^8) / ((1-x)^6*(1-3*x+x^2)). - Colin Barker, Feb 19 2016

From G. C. Greubel, Jun 16 2025: (Start)

a(n) = A000032(2*n+8) - (1/30)*(1410 + 1351*n + 655*n^2 + 230*n^3 + 20*n^4 + 24*n^5) + [n=2].

E.g.f.: exp(3*x/2)*( 47*cosh(sqrt(5)*x/2) + 21*sqrt(5)*sinh(sqrt(5)*x/2) ) + x^2/2 - (1/30)*(1410 + 2280*x + 1845*x^2 + 950*x^3 + 260*x^4 + 24*x^5)*exp(x). (End)

Mathematica

Table[LucasL[2*n+8] -(1410 +1351*n +655*n^2 +230*n^3 +20*n^4 +24*n^5)/30 + Boole[n==2], {n, 2, 50}] (* G. C. Greubel, Jun 16 2025 *)

Prog

(PARI) Vec(x^2*(1+103*x^2-30*x^3+69*x^4-73*x^5+34*x^6-9*x^7+x^8)/((1-x)^6*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 19 2016
(Magma)
A027018:= func< n | n eq 2 select 1 else Lucas(2*n+8) -(1410 +1351*n +655*n^2 +230*n^3 +20*n^4 +24*n^5)/30 >;
[A027018(n): n in [2..50]]; // G. C. Greubel, Jun 16 2025
(SageMath)
def A027018(n): return lucas_number2(2*n+8, 1, -1) -(1410 +1351*n +655*n^2 +230*n^3 +20*n^4 +24*n^5)//30 + int(n==2)
print([A027018(n) for n in range(2, 51)]) # G. C. Greubel, Jun 16 2025

Crossrefs

Cf. A000032, A027011.

Sequence in context: A296017 A218350 A337672 * A326012 A089916 A143000

Adjacent sequences: A027015 A027016 A027017 * A027019 A027020 A027021

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved