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

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

Offset: 0

Author

Jianing Song, Jan 15 2023

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

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).

Programs

Mathematica

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

PARI

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

Python

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

Formula

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