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a(1)=17; for n>1, a(n) = (a(n-1)^2 - 1)/2 if n is even, a(n-1) + 1 if n is odd.
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%I #22 May 29 2024 12:16:25

%S 17,144,145,10512,10513,55261584,55261585,1526921388356112,

%T 1526921388356113,1165744463109679828308252234384,

%U 1165744463109679828308252234385,679480076635437837059150531810555804350472205781672488164112,679480076635437837059150531810555804350472205781672488164113

%N a(1)=17; for n>1, a(n) = (a(n-1)^2 - 1)/2 if n is even, a(n-1) + 1 if n is odd.

%C {17, 144, 145}, {145, 10512, 10513}, {10513, 55261584, 55261585}, ... are sides {a < b < c} of the right triangles, with hypotenuse c = b + 1.

%H Eric Chen, <a href="/A304207/b304207.txt">Table of n, a(n) for n = 1..21</a>

%t nxt[{n_,a_}]:={n+1,If[OddQ[n],(a^2-1)/2,a+1]}; NestList[nxt,{1,17},20][[All,2]] (* _Harvey P. Dale_, Mar 27 2021 *)

%o (PARI) a(n) = if(n==1,17,if(n%2,a(n-1)+1,(a(n-1)^2 - 1)/2)) \\ _Eric Chen_, Jun 09 2018

%Y Same basic form as A076601, A076602, A076603, and A076604.

%K nonn

%O 1,1

%A _Benjamin Knight_, May 08 2018