A189374 Expansion of 1/((1-x)^5*(x^2+x+1)^3).

1, 2, 3, 7, 11, 15, 25, 35, 45, 65, 85, 105, 140, 175, 210, 266, 322, 378, 462, 546, 630, 750, 870, 990, 1155, 1320, 1485, 1705, 1925, 2145, 2431, 2717, 3003, 3367, 3731, 4095, 4550, 5005, 5460, 6020, 6580, 7140, 7820

Offset

0,2

Comments

The Ca1(n) and Ze3(n) triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of these triangle sums see A180662.

Links

Table of n, a(n) for n=0..42.

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

Formula

a(n) = (2*a(n-1) + 2*a(n-2) + (8+n)*a(n-3))/n with a(0)=1, a(1)=2, a(2)=3 and a(3)=7.

a(n) = sum(A011779(n-k)*A049347(k), k=0..n).

Ca1(n) = A189374(n-3) - A189374(n-4) - A189374(n-6) + 2*A189374(n-7).

Ze3(n) = 2*A189374(n-3) - A189374(n-4) - 2*A189374(n-6) + 5*A189374(n-7) with A189374(n)=0 for n <= -1.

a(n) = (floor(n/3)+1)*(floor(n/3)+2)*(floor(n/3)+3)*(3*floor(n/3)+4*(4-(3*floor((n+3)/3)-n)))/24. - Luce ETIENNE, Jun 29 2015

Maple

a:= proc(n) option remember; `if` (n<4, [1, 2, 3, 7][n+1], (2*a(n-1) +2*a(n-2) +(8+n) *a(n-3))/n) end: seq (a(n), n=0..50);

Crossrefs

Cf. A139600, A189375, A189376.

Sequence in context: A174060 A285278 A092353 * A180516 A100963 A342029

Adjacent sequences: A189371 A189372 A189373 * A189375 A189376 A189377

Keyword

easy,nonn

Author

Johannes W. Meijer, Apr 29 2011

Status

approved