A189376 Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^2).

1, 3, 6, 10, 17, 27, 40, 56, 78, 106, 140, 180, 230, 290, 360, 440, 535, 645, 770, 910, 1071, 1253, 1456, 1680, 1932, 2212, 2520, 2856, 3228, 3636, 4080, 4560, 5085, 5655, 6270, 6930, 7645, 8415, 9240, 10120, 11066, 12078

Offset

0,2

Comments

The Gi2 triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of the Gi2 and other triangle sums see A180662.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2,-6,6,-2,-1,3,-3,1).

Formula

a(n) = sum(A144678(n-k), k=0..n).

Gi2(n) = A189376(n-1) - A189376(n-2) - A189376(n-5) + 2*A189376(n-6) with A189376(n)=0 for n <= -1.

a(0)=1, a(1)=3, a(2)=6, a(3)=10, a(4)=17, a(5)=27, a(6)=40, a(7)=56, a(8)=78, a(9)=106, a(10)=140, a(n)=3*a(n-1)-3*a(n-2)+a(n-3)+ 2*a(n-4)- 6*a(n-5)+6*a(n-6)-2*a(n-7)-a(n-8)+3*a(n-9)-3*a(n-10)+a(n-11). - Harvey P. Dale, Apr 12 2015

Maple

a:= n-> coeff (series (1/((1-x)^5*(x^3+x^2+x+1)^2), x, n+1), x, n):
seq (a(n), n=0..50);

Mathematica

CoefficientList[Series[1/((1-x)^5(x^3+x^2+x+1)^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 1, 2, -6, 6, -2, -1, 3, -3, 1}, {1, 3, 6, 10, 17, 27, 40, 56, 78, 106, 140}, 50] (* Harvey P. Dale, Apr 12 2015 *)

Crossrefs

Cf. A139600, A189374, A189375.

Sequence in context: A308699 A286304 A005045 * A069241 A092263 A259968

Adjacent sequences: A189373 A189374 A189375 * A189377 A189378 A189379

Keyword

easy,nonn

Author

Johannes W. Meijer, Apr 29 2011

Status

approved