A359499 -id:A359499 - cp's OEIS frontend

A359498 a(n) = ((2*n+1)^8 - 1)/32.

0, 205, 12207, 180150, 1345210, 6698715, 25491585, 80090332, 217992420, 530736345, 1181964355, 2447218290, 4768371582, 8825923015, 15632700405, 26652844920, 43950269320, 70371105957, 109764982935, 167250289390, 249528913410, 365256258675, 525472668457, 744102708180

Offset: 0

Jianing Song, Jan 03 2023

a(n) and A000217(n) have the same parity.

Jianing Song, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. {((2*n+1)^2^k - 1)/2^(k+2)}: A000217 (k=1), A219086 (k=2), this sequence (k=3), A359499 (k=4).

((2*Range[0, 25] + 1)^8 - 1)/32 (* Paolo Xausa, Jan 23 2025 *)

PARI
```
a(n) = ((2*n+1)^8 - 1)/32
```

def A359498(n): return ((n<<1)+1)**8-1>>5 # Chai Wah Wu, Jan 15 2023

a(n) = A000217(n) * A219086(n) * A175110(n) = A219086(n) * A175110(n).

A359844 a(n) = ((2*n+1)^8 + 1)/2.

Original entry on oeis.org

1, 3281, 195313, 2882401, 21523361, 107179441, 407865361, 1281445313, 3487878721, 8491781521, 18911429681, 39155492641, 76293945313, 141214768241, 250123206481, 426445518721, 703204309121, 1125937695313, 1756239726961, 2676004630241, 3992462614561, 5844100138801

Offset: 0

Jianing Song, Jan 15 2023

Jianing Song, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. {((2*n+1)^k + 1)/2}: A000012 (k=0), A001477 (k=1), A219086 (k=2), A050492 (k=3), A175110 (k=4), A175113 (k=6), this sequence (k=8).

((2*Range[0, 25] + 1)^8 + 1)/2 (* Paolo Xausa, Jan 23 2025 *)

PARI
```
a(n) = ((2*n+1)^8 + 1)/2
```

def A359844(n): return ((n<<1)+1)**8+1>>1 # Chai Wah Wu, Jan 15 2023

a(n) = A359499(n)/A359498(n) = 16 * A359498(n) + 1.

cp's OEIS Frontend

A359498 a(n) = ((2*n+1)^8 - 1)/32.

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