A075112 a(n)=Sum((-1)^(i+Floor(n/2))S(2i+e),(i=0,..,Floor(n/2))), where S(n) are generalized Tetranacci numbers (A073817) and e=(1/2)(1-(-1)^n).

4, 1, -1, 6, 16, 20, 35, 79, 156, 288, 552, 1077, 2079, 3994, 7696, 14848, 28623, 55159, 106320, 204952, 395060, 761489, 1467815, 2829318, 5453688, 10512308, 20263123, 39058439, 75287564, 145121432, 279730552, 539197989, 1039337543, 2003387514, 3861653592, 7443576640, 14347955295

Offset

0,1

Comments

a(n) is the convolution of S(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594.

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 2, 2, 1, 1).

Formula

a(n)=a(n-1)+2a(n-3)+2a(n-4)+a(n-5)+a(n-6), a(0)=4, a(1)=1, a(2)=-1, a(3)=6, a(4)=16, a(5)=20. G.f.: (4 - 3*x - 2*x^2 - x^3)/(1 - x - 2*x^3 - 2*x^4 - x^5 - x^6).

Mathematica

CoefficientList[Series[(4 - 3*x - 2*x^2 - x^3)/(1 - x - 2*x^3 - 2*x^4 - x^5 - x^6), {x, 0, 40}], x]
LinearRecurrence[{1, 0, 2, 2, 1, 1}, {4, 1, -1, 6, 16, 20}, 40] (* Harvey P. Dale, Mar 09 2013 *)

Crossrefs

Cf. A073817, A056594, A074662, A074677, A074678, A075111.

Sequence in context: A131399 A069322 A208332 * A202687 A046554 A010321

Adjacent sequences: A075109 A075110 A075111 * A075113 A075114 A075115

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2002

Status

approved