A227855 -id:A227855 - cp's OEIS frontend

A272298 a(n) = n^4 + 324.

324, 325, 340, 405, 580, 949, 1620, 2725, 4420, 6885, 10324, 14965, 21060, 28885, 38740, 50949, 65860, 83845, 105300, 130645, 160324, 194805, 234580, 280165, 332100, 390949, 457300, 531765, 614980, 707605, 810324, 923845, 1048900, 1186245, 1336660, 1500949, 1679940, 1874485, 2085460

Offset: 0

Bruno Berselli, Apr 25 2016

This is the case k=3 of Sophie Germain's Identity n^4+(2*k^2)^2 = ((n-k)^2+k^2)*((n+k)^2+k^2).

Bruno Berselli, Table of n, a(n) for n = 0..1000
Wikipedia, Sophie Germain's Identity.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A005917.
Subsequence of A227855.
Cf. A000583 (k=0), A057781 (k=1), A272297 (k=2).

Magma
```
[n^4+324: n in [0..40]];
```

Table[n^4 + 324, {n, 0, 40}]
LinearRecurrence[{5,-10,10,-5,1},{324,325,340,405,580},40] (* Harvey P. Dale, Jan 20 2021 *)

Maxima
```
makelist(n^4+324, n, 0, 40);
```
PARI
```
vector(40, n, n--; n^4+324)
```
Python
```
[n**4+324 for n in range(40)]
```

for n in range(0, 10**5):print(n**4+324,end=", ") # Soumil Mandal, Apr 30 2016

Sage
```
[n^4+324 for n in (0..40)]
```

O.g.f.: (324 - 1295*x + 1955*x^2 - 1285*x^3 + 325*x^4)/(1 - x)^5. [Corrected by Georg Fischer, May 23 2019]
E.g.f.: (324 + x + 7*x^2 + 6*x^3 + x^4)*exp(x).
a(n) = (n^2 - 18)^2 + (6*n)^2.

A272297 a(n) = n^4 + 64.

Original entry on oeis.org

64, 65, 80, 145, 320, 689, 1360, 2465, 4160, 6625, 10064, 14705, 20800, 28625, 38480, 50689, 65600, 83585, 105040, 130385, 160064, 194545, 234320, 279905, 331840, 390689, 457040, 531505, 614720, 707345, 810064, 923585, 1048640, 1185985, 1336400, 1500689, 1679680, 1874225, 2085200

Offset: 0

Bruno Berselli, Apr 25 2016

This is the case k=2 of Sophie Germain's Identity n^4+(2*k^2)^2 = ((n-k)^2+k^2)*((n+k)^2+k^2).

Bruno Berselli, Table of n, a(n) for n = 0..1000
Wikipedia, Sophie Germain's Identity.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A005917.
Subsequence of A227855.
Cf. A000583 (k=0), A057781 (k=1), A272298 (k=3).

Magma
```
[n^4+64: n in [0..40]];
```
Mathematica
```
Table[n^4 + 64, {n, 0, 40}]
```
Maxima
```
makelist(n^4+64, n, 0, 40);
```
PARI
```
vector(40, n, n--; n^4+64)
```
Python
```
[n**4+64 for n in range(40)]
```

for n in range(0,10**5):print(n**4+64) # Soumil Mandal, Apr 30 2016

Sage
```
[n^4+64 for n in (0..40)]
```

O.g.f.: (64 - 255*x + 395*x^2 - 245*x^3 + 65*x^4)/(1 - x)^5.
E.g.f.: (64 + x + 7*x^2 + 6*x^3 + x^4)*exp(x).
a(n) = (n^2 - 8)^2 + (4*n)^2.

cp's OEIS Frontend

A272298 a(n) = n^4 + 324.

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A272297 a(n) = n^4 + 64.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Python

Python

Sage

Formula