A054686 Multiset consisting of squares and triangular numbers.

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, 105, 120, 121, 136, 144, 153, 169, 171, 190, 196, 210, 225, 231, 253, 256, 276, 289, 300, 324, 325, 351, 361, 378, 400, 406, 435, 441, 465, 484, 496, 528

Offset: 1

Author

Michael Somos, Apr 19 2000

Keywords

• nonn
• easy

Comments

Terms of A001110 occur twice. [Reinhard Zumkeller, Aug 03 2011]

References

• 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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005214, A000217, A000290.

Programs

Haskell

a054686_list = merge a000290_list a000217_list where
   merge xs'@(x:xs) ys'@(y:ys)
     | x <= y    = x : merge xs ys'
     | otherwise = y : merge xs' ys
-- Reinhard Zumkeller, Aug 03 2011

Mathematica

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 *)

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

Extensions

Offset fixed by Reinhard Zumkeller, Aug 04 2011