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

Author

Jianing Song, Jan 03 2023

Keywords

• nonn
• easy

Comments

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

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

Programs

Mathematica

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

PARI

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

Python

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

Formula

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