A359844 - OEIS

%I #16 Jan 23 2025 03:36:44

%S 1,3281,195313,2882401,21523361,107179441,407865361,1281445313,

%T 3487878721,8491781521,18911429681,39155492641,76293945313,

%U 141214768241,250123206481,426445518721,703204309121,1125937695313,1756239726961,2676004630241,3992462614561,5844100138801

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

%H Jianing Song, <a href="/A359844/b359844.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

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

%t ((2*Range[0, 25] + 1)^8 + 1)/2 (* _Paolo Xausa_, Jan 23 2025 *)

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

%o (Python)

%o def A359844(n): return ((n<<1)+1)**8+1>>1 # _Chai Wah Wu_, Jan 15 2023

%Y 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).

%K nonn,easy

%O 0,2

%A _Jianing Song_, Jan 15 2023