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A005214 Triangular numbers together with squares. 9
1, 3, 4, 6, 9, 10, 15, 16, 21, 25, 28, 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, 529, 561, 576, 595, 625, 630, 666, 676 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A010052(a(n)) + A010054(a(n)) > 0, A010052(a(A193714(n))) = 1, A010054(a(A193715(n))) = 1. [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

Eric Weisstein's World of Mathematics, Square Triangular Number

MATHEMATICA

With[{upto=700}, Module[{maxs=Floor[Sqrt[upto]], maxt=Floor[(Sqrt[8upto+1]- 1)/2]}, Union[Join[Range[maxs]^2, Table[(n(n+1))/2, {n, maxt}]]]]] (* Harvey P. Dale, Sep 17 2011 *)

PROG

(Haskell)

a005214 n = a005214_list !! (n-1)

a005214_list = tail $ merge a000290_list a000217_list where

   merge xs'@(x:xs) ys'@(y:ys)

     | x < y     = x : merge xs 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), n, n^2), vector(floor(sqrt(2+2*lim)-1/2), n, n*(n+1)/2)), , 8) \\ Charles R Greathouse IV, Aug 04 2011

CROSSREFS

Cf. A054686.

Cf. A001110; union of A000290 and A000217 (without initial 0); A117704 (first differences), A193711 (partial sums); A193748, A193749 (partitions into).

Sequence in context: A130904 A034706 A054686 * A124093 A025061 A037969

Adjacent sequences:  A005211 A005212 A005213 * A005215 A005216 A005217

KEYWORD

nonn,easy

AUTHOR

Russ Cox

STATUS

approved

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Last modified April 17 03:13 EDT 2014. Contains 240628 sequences.