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A140978 Repeat (n+1)^2 n times.

%I A140978 #20 Nov 07 2024 20:37:29
%S A140978 4,9,9,16,16,16,25,25,25,25,36,36,36,36,36,49,49,49,49,49,49,64,64,64,
%T A140978 64,64,64,64,81,81,81,81,81,81,81,81,100,100,100,100,100,100,100,100,
%U A140978 100,121,121,121,121,121,121,121,121,121,121
%N A140978 Repeat (n+1)^2 n times.
%C A140978 See A093995.
%C A140978 Frenicle writes the entries in the form a(n) = A055096(n)-A133819(n), with the flattened index view of A133819: 4=5-1, 9=10-1, 9=13-4, 16=17-1, 16=20-4, 16=25-9 etc.
%C A140978 Also triangle T(n, k) = (n+1)^2, 1<=k<=n. - _Michel Marcus_, Feb 03 2013
%H A140978 Reinhard Zumkeller, <a href="/A140978/b140978.txt">Rows n = 1..120 of triangle, flattened</a>
%H A140978 M. de Frenicle, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k5493994j/">Methode pour trouver la solutions des problemes par les exclusions</a>, in: Divers ouvrages des mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44, table page 11.
%F A140978 a(n)=(A003057(n+1))^2. - _R. J. Mathar_, Aug 25 2008
%t A140978 Table[PadRight[{},n,(n+1)^2],{n,10}]//Flatten (* _Harvey P. Dale_, Oct 10 2019 *)
%o A140978 (Haskell)
%o A140978 a140978 n k = a140978_tabl !! (n-1) !! (k-1)
%o A140978 a140978_row n = a140978_tabl !! (n-1)
%o A140978 a140978_tabl = map snd $ iterate
%o A140978                (\(i, xs@(x:_)) -> (i + 2, map (+ i) (x:xs))) (5, [4])
%o A140978 -- _Reinhard Zumkeller_, Mar 23 2013
%o A140978 (Python)
%o A140978 from math import isqrt
%o A140978 def A140978(n): return ((m:=isqrt(k:=n<<1))+(k>m*(m+1))+1)**2 # _Chai Wah Wu_, Nov 07 2024
%Y A140978 Cf. A000290.
%K A140978 nonn,easy,tabl
%O A140978 1,1
%A A140978 _Paul Curtz_, Aug 17 2008