A258837 a(n) = 1 - n^2.

1, 0, -3, -8, -15, -24, -35, -48, -63, -80, -99, -120, -143, -168, -195, -224, -255, -288, -323, -360, -399, -440, -483, -528, -575, -624, -675, -728, -783, -840, -899, -960, -1023, -1088, -1155, -1224, -1295, -1368, -1443, -1520, -1599, -1680, -1763, -1848

Offset: 0

Author

Vincenzo Librandi, Jun 12 2015

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A067998, A131386, A007531.

Sequences of the type 1-n^k: A024000 (k=1), this sequence (k=2), A024001 (k=3), A024002 (k=4), A024003 (k=5), A024004 (k=6), A024005 (k=7), A024006 (k=8), A024007 (k=9), A024008 (k=10), A024009 (k=11), A024010 (k=12).

Programs

Magma

[1-n^2: n in [0..50]];

Magma

I:=[1,0,-3]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];

Mathematica

Table[1 - n^2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 0, -3}, 50]

PARI

my(x='x+O('x^50)); Vec((1-3*x)/(1-x)^3) \\ G. C. Greubel, May 11 2017

Formula

G.f.: (1-3*x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = -A067998(n+1). - Joerg Arndt, Jun 13 2015

a(n) = (-1)^n*A131386(n+1). - Bruno Berselli, Jun 15 2015

E.g.f.: (1 - x - x^2)*exp(x). - G. C. Greubel, May 11 2017

Sum_{n>=2} 1/a(n) = -3/4. - Amiram Eldar, Feb 17 2023