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

1,5

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A005214, A000217, A000290.

Sequence in context: A130904 A034706 A245810 * A005214 A268110 A124093

Adjacent sequences: A054683 A054684 A054685 * A054687 A054688 A054689

Keyword

nonn,easy

Author

Michael Somos, Apr 19 2000

Extensions

Offset fixed by Reinhard Zumkeller, Aug 04 2011

Status

approved