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A145131 Expansion of x/((1 - x - x^4)*(1 - x)^2). 5
0, 1, 3, 6, 10, 16, 25, 38, 56, 81, 116, 165, 233, 327, 457, 637, 886, 1230, 1705, 2361, 3267, 4518, 6245, 8629, 11920, 16463, 22734, 31390, 43338, 59830, 82594, 114015, 157385, 217248, 299876, 413926, 571347, 788632, 1088546, 1502511, 2073898, 2862571 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The coefficients of the recursion for a(n) are given by the 3rd row of A145152.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 3a(n-1) -3a(n-2) +a(n-3) +a(n-4) -2a(n-5) +a(n-6).

EXAMPLE

a(7) = 38 = 3*25 -3*16 +10 +6 -2*3 +1.

MAPLE

col:= proc(k) local l, j, M, n; l:= `if` (k=0, [1, 0, 0, 1], [seq(coeff( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix(nops(l), (i, j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if`(k=0, n->(M^n)[2, 3], n->(M^n)[1, 2]) end: a:= col(3): seq(a(n), n=0..40);

MATHEMATICA

Series[x/((1-x-x^4)*(1-x)^2), {x, 0, 50}] // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 13 2014 *)

LinearRecurrence[{3, -3, 1, 1, -2, 1}, {0, 1, 3, 6, 10, 16}, 50] (* Harvey P. Dale, Aug 08 2015 *)

PROG

(PARI) concat(0, Vec(1/(1-x-x^4)/(1-x)^2+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

CROSSREFS

3rd column of A145153. Cf. A145152.

Sequence in context: A025222 A011902 A025004 * A265072 A152009 A255875

Adjacent sequences:  A145128 A145129 A145130 * A145132 A145133 A145134

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Oct 03 2008

STATUS

approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)