A108923 Expansion of 1/((x^8+1)*(1-x)^3).

1, 3, 6, 10, 15, 21, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 109, 119, 130, 142, 155, 169, 184, 200, 216, 232, 248, 264, 280, 296, 312, 328, 345, 363, 382, 402, 423, 445, 468, 492, 516, 540, 564, 588, 612, 636, 660, 684, 709, 735, 762, 790, 819, 849, 880, 912

Offset

0,2

Comments

Triangular numbers A000217 start: 0,1,3,6,10,15,21,28,36,45,55

Links

Table of n, a(n) for n=0..55.

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1, 0, 0, 0, 0, -1, 3, -3, 1).

Formula

a(0)=1, a(1)=3, a(2)=6, a(3)=10, a(4)=15, a(5)=21, a(6)=28, a(7)=36, a(8)=44, a(9)=52, a(10)=60, a(n)=3*a(n-1)-3*a(n-2)+a(n-3)-a(n-8)+ 3*a(n-9)- 3*a(n-10)+a (n-11). - Harvey P. Dale, Jan 28 2015

Maple

seriestolist(series(1/((x^8+1)*(x-1)^3), x=0, 100));

Mathematica

CoefficientList[Series[1/((1-x)^3 (1+x^8)), {x, 0, 60}], x]  (* or *) LinearRecurrence[{3, -3, 1, 0, 0, 0, 0, -1, 3, -3, 1}, {1, 3, 6, 10, 15, 21, 28, 36, 44, 52, 60}, 60] (* Harvey P. Dale, Jan 28 2015 *)

Crossrefs

Cf. A000217.

Sequence in context: A130487 A231684 A363777 * A033441 A338334 A107082

Adjacent sequences: A108920 A108921 A108922 * A108924 A108925 A108926

Keyword

easy,nonn

Author

Creighton Dement, Jul 17 2005

Extensions

Definition corrected by Harvey P. Dale, Jan 28 2015

Status

approved