A024009 -id:A024009 - cp's OEIS frontend

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

Vincenzo Librandi, Jun 12 2015

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

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).

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

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]];

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

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

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

A258812 a(n) = n^11 - 1.

Original entry on oeis.org

0, 2047, 177146, 4194303, 48828124, 362797055, 1977326742, 8589934591, 31381059608, 99999999999, 285311670610, 743008370687, 1792160394036, 4049565169663, 8649755859374, 17592186044415, 34271896307632, 64268410079231, 116490258898218, 204799999999999

Offset: 1

Vincenzo Librandi, Jun 11 2015

Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A024009.

Cf. similar sequences listed in A258807.

Magma
```
[n^11-1: n in [1..40]];
```

Table[n^11 - 1, {n, 33}] (* or *) LinearRecurrence[{12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1}, {0, 2047, 177146, 4194303, 48828124, 362797055, 1977326742, 8589934591, 31381059608, 99999999999, 285311670610, 743008370687}, 40]

G.f.: x^2* (2047 + 152582*x + 2203653*x^2 + 9737784*x^3 + 15724710*x^4 + 9737652*x^5 + 2203818*x^6 + 152472*x^7 + 2091*x^8 - 10*x^9 + x^10) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12).
a(n) = -A024009(n). [Bruno Berselli, Jun 12 2015]

cp's OEIS Frontend

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

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A258812 a(n) = n^11 - 1.

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Author

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Magma

Mathematica

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