A291681 First differences of A067046.

1, 8, 0, 25, -7, 56, -24, 105, -55, 176, -104, 273, -175, 400, -272, 561, -399, 760, -560, 1001, -759, 1288, -1000, 1625, -1287, 2016, -1624, 2465, -2015, 2976, -2464, 3553, -2975, 4200, -3552, 4921, -4199, 5720, -4920, 6601, -5719, 7568, -6600, 8625, -7567, 9776, -8624

Offset: 1

Author

Enrique Navarrete, Sep 04 2017

Keywords

• sign
• easy

Comments

a(2n) > 0 and a(2n+1) < 0 for all n >= 2.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-3,-3,1,1).

Crossrefs

Cf. A067046.

Programs

Maple

a:= n-> `if`(irem(n-1, 2, 'r')=0, -(r-1)*(2*r+3)*(r+1)/3
                                , (2*r+3)*(r+4)*(r+2)/3):
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 04 2017

PARI

Vec(x*(1 + 9*x + 5*x^2 - 2*x^3 - 3*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^4) + O(x^60)) \\ Colin Barker, Sep 29 2017

Formula

a(n) = A067046(n+1) - A067046(n).

G.f.: -x*(x^6+x^5-3*x^4-2*x^3+5*x^2+9*x+1)/((x-1)^3*(x+1)^4). - Alois P. Heinz, Sep 04 2017

From Colin Barker, Sep 29 2017: (Start)

a(n) = (n^3 + 9*n^2 + 20*n + 12) / 12 for n even.

a(n) = (-n^3 + 7*n + 6) / 12 for n odd.

(End)