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a(1) = 4; for n >= 1, a(n+1) = 4 + binomial(a(n), 2).
1

%I #15 Sep 08 2022 08:45:38

%S 4,10,49,1180,695614,241939070695,29267256964259134356169,

%T 428286165105987400438217763289707431507000200

%N a(1) = 4; for n >= 1, a(n+1) = 4 + binomial(a(n), 2).

%C Arises in a geometry problem: see link.

%C Next term (a(9)) has 89 digits. - _Emeric Deutsch_, Jun 20 2009

%H Antreas P. Hatzipolakis, <a href="http://groups.yahoo.com/group/Anopolis/message/103">Concurrent NPC's</a>.

%H Antreas P. Hatzipolakis, <a href="/A151611/a151611.txt">Concurrent NPCs</a>, digest of 4 messages in Anopolis Yahoo group, May 23, 2009 - Aug 26, 2016. [Cached copy]

%p a[1] := 4: for n to 7 do a[n+1] := 4+binomial(a[n], 2) end do: seq(a[n], n = 1 .. 8); # _Emeric Deutsch_, Jun 20 2009

%o (Magma) [n eq 1 select 4 else 4+Binomial(Self(n-1),2):n in [1..8]]; // _Marius A. Burtea_, Nov 16 2019

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, May 28 2009

%E More terms from _Emeric Deutsch_, Jun 20 2009