A144413 a(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) * A000931(n-k+4).

0, 1, -1, 1, 0, -3, 10, -24, 49, -89, 145, -208, 245, -174, -176, 1121, -3185, 7137, -13920, 24301, -37926, 51256, -53615, 20407, 97265, -386224, 984549, -2083934, 3896480, -6537023, 9734175, -12231999, 10690624, 2126301, -39992150, 126414472, -297132815, 598577351, -1075051951, 1730868336, -2443923755

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (-3,-2,1).

Formula

From R. J. Mathar, Jan 21 2009: (Start)

a(n) = -3*a(n-1) - 2*a(n-2) + a(n-3).

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

Mathematica

(* First program *)
b[n_]:= b[n]= If[n==0, 0, If[n<3, 1, b[n-2] +b[n-3]]];
a[n_]:= Sum[(-1)^m*Binomial[n, m]*b[n-m], {m, 0, n}];
Table[a[n], {n, 0, 50}]
(* Second program *)
LinearRecurrence[{-3, -2, 1}, {0, 1, -1}, 51] (* G. C. Greubel, Mar 27 2021 *)

Prog

(Magma) I:=[0, 1, 1]; [n le 3 select I[n] else -3*Self(n-1) -2*Self(n-2) +Self(n-3): n in [1..51]]; // G. C. Greubel, Mar 27 2021
(Sage)
@CachedFunction
def A000931(n): return 1 if n==0 else sum( binomial(k, n-2*k-3) for k in (0..floor((n-3)/2)))
def A144413(n): return sum( (-1)^k*binomial(n, k)*A000931(n-k+4) for k in (0..n))
[A144413(n) for n in (0..50)] # G. C. Greubel, Mar 27 2021

Crossrefs

Cf. A000073, A000931, A073358.

Sequence in context: A259443 A293405 A029880 * A033811 A062446 A053208

Adjacent sequences: A144410 A144411 A144412 * A144414 A144415 A144416

Keyword

sign,easy

Author

Roger L. Bagula and Gary W. Adamson, Sep 30 2008

Extensions

Terms a(30) onward added and edited by G. C. Greubel, Mar 27 2021

Status

approved