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Multiset consisting of squares and triangular numbers.
5

%I #21 Apr 30 2014 01:34:21

%S 0,0,1,1,3,4,6,9,10,15,16,21,25,28,36,36,45,49,55,64,66,78,81,91,100,

%T 105,120,121,136,144,153,169,171,190,196,210,225,231,253,256,276,289,

%U 300,324,325,351,361,378,400,406,435,441,465,484,496,528

%N Multiset consisting of squares and triangular numbers.

%C Terms of A001110 occur twice. [_Reinhard Zumkeller_, Aug 03 2011]

%D Hofstadter, D. R., Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, (together with the Fluid Analogies Research Group), NY: Basic Books, 1995. p. 15.

%H Reinhard Zumkeller, <a href="/A054686/b054686.txt">Table of n, a(n) for n = 1..10000</a>

%t stnos[max_]:=Module[{sqmax=Floor[Sqrt[max]],trmax=Floor[(Sqrt[ 8max+1]- 1)/2]}, Sort[Join[Range[0,sqmax]^2,Accumulate[Range[0,trmax]]]]]; stnos[ 528] (* _Harvey P. Dale_, Feb 06 2012 *)

%o (Haskell)

%o a054686_list = merge a000290_list a000217_list where

%o merge xs'@(x:xs) ys'@(y:ys)

%o | x <= y = x : merge xs ys'

%o | otherwise = y : merge xs' ys

%o -- _Reinhard Zumkeller_, Aug 03 2011

%o (PARI) upTo(lim)=vecsort(concat(vector(sqrtint(lim\1)+1,n,(n-1)^2),vector(floor(sqrt(2+2*lim)+1/2),n,n*(n-1)/2))) \\ _Charles R Greathouse IV_, Aug 04 2011

%Y Cf. A005214, A000217, A000290.

%K nonn,easy

%O 1,5

%A _Michael Somos_, Apr 19 2000

%E Offset fixed by _Reinhard Zumkeller_, Aug 04 2011