A074662 -id:A074662

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A075111

a(n)=Sum((-1)^(i+Floor(n/2))T(2i+e),(i=0,..,Floor(n/2))), where T(n) are tribonacci numbers (A000073) and e=(1/2)(1-(-1)^n).

+10
1

0, 1, 1, 1, 3, 6, 10, 18, 34, 63, 115, 211, 389, 716, 1316, 2420, 4452, 8189, 15061, 27701, 50951, 93714, 172366, 317030, 583110, 1072507, 1972647, 3628263, 6673417, 12274328, 22576008, 41523752, 76374088, 140473849, 258371689

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

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

LINKS

Table of n, a(n) for n=0..34.

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

FORMULA

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

MATHEMATICA

CoefficientList[Series[x/(1 - x - 2*x^3 - x^4 - x^5), {x, 0, 40}], x]

CROSSREFS

Cf. A000073, A056594, A074662, A074677, A074678.

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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).

+10
0

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

(list; graph; refs; listen; history; text; internal format)

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 *)