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A057944
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Largest triangular number less than or equal to n; write m-th triangular number m+1 times.
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9
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0, 1, 1, 3, 3, 3, 6, 6, 6, 6, 10, 10, 10, 10, 10, 15, 15, 15, 15, 15, 15, 21, 21, 21, 21, 21, 21, 21, 28, 28, 28, 28, 28, 28, 28, 28, 36, 36, 36, 36, 36, 36, 36, 36, 36, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 66, 66, 66, 66, 66, 66
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Reinhard Zumkeller, Rows n=0..100 of triangle, flattened
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FORMULA
| a(n) =floor((sqrt(1+8*n)-1)/2)*floor((sqrt(1+8*n)+1)/2)/2 =(trinv(n)*(trinv(n)-1))/2 =A000217(A003056(n)) =n-A002262(n)
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EXAMPLE
| a(35)=28 since 28 and 36 are successive triangular numbers and 28<=35<36
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MAPLE
| A057944 := proc(n)
k := (-1+sqrt(1+8*n))/2 ;
k := floor(k) ;
k*(k+1)/2 ;
end proc; # R. J. Mathar, Nov 05 2011
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MATHEMATICA
| f[n_] := Block[{a = Floor@ Sqrt[1 + 8 n]}, Floor[(a - 1)/2]*Floor[(a + 1)/2]/2]; Array[f, 72, 0]
t0=0; t1=1; k=1; Table[If[n < t1, t0, k++; t0=t1; t1=t1+k; t0], {n, 0, 72}]
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PROG
| (Haskell)
a057944 n = a057944_list !! n -- common flat access
a057944_list = concat a057944_tabl
a057944' n k = a057944_tabl !! n !! k -- access when seen as a triangle
a057944_row n = a057944_tabl !! n
a057944_tabl = zipWith ($) (map replicate [1..]) a000217_list
-- Reinhard Zumkeller, Feb 03 2012
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CROSSREFS
| Cf. A000217, A003056, A003056, A056944, A057945.
Cf. A127739.
Sequence in context: A108581 A073080 A171601 * A080607 A013322 A177821
Adjacent sequences: A057941 A057942 A057943 * A057945 A057946 A057947
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KEYWORD
| easy,nonn,tabl,changed
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Oct 05 2000
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EXTENSIONS
| Keyword tabl added by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 03 2012
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