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Values square, differences triangular.
4

%I #23 Nov 14 2022 20:02:20

%S 0,1,4,25,196,1681,2116,18769,168100,1510441,13586596,14577124,

%T 15856324,16120225,16289296,16736281,150601984,151782400,1365967681,

%U 1368334081,1393379584,1640655025,1649578225,1669212736,1725737764

%N Values square, differences triangular.

%H Donovan Johnson, <a href="/A036449/b036449.txt">Table of n, a(n) for n = 1..145</a>

%t triangularQ[n_] := IntegerQ[Sqrt[8n + 1]]; a[1] = 0; a[n_] := a[n] = (b = Sqrt[a[n-1]]; While[b++; ! triangularQ[b^2 - a[n-1]]]; b^2); Table[a[n], {n, 1, 25}] (* _Jean-François Alcover_, Oct 04 2011 *)

%o (Haskell)

%o a036449 n = a036449_list !! (n-1)

%o a036449_list = map fst listsOfValsAndDiffs

%o a189475 n = a189475_list !! (n-1)

%o a189475_list = tail $ map snd listsOfValsAndDiffs

%o listsOfValsAndDiffs = (0,1) : f (0,1) where

%o f (x,y) = (u,v) : f (u,v) where

%o u = x + v

%o v = head $ dropWhile ((== 0) . a010052 . (+ x)) $ tail a000217_list

%o -- _Reinhard Zumkeller_, Apr 23 2011

%o (Python)

%o from itertools import count, islice

%o from sympy import integer_nthroot

%o def A036449_gen(): # generator of terms

%o yield (a:=0)

%o for n in count(1):

%o if integer_nthroot(((b:=n**2)-a<<3)+1,2)[1]:

%o yield (a:=b)

%o A036449_list = list(islice(A036449_gen(),20)) # _Chai Wah Wu_, Nov 14 2022

%Y Cf. A000217, A010052, A000290, A010054, A189475 (first differences).

%K nonn,nice

%O 1,3

%A _David W. Wilson_

%E Offset corrected by _Donovan Johnson_, Jan 20 2011