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A056231
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Form an array with 3 rows: row 1 begins with 1; all rows are increasing; each entry is sum of 2 entries above it; each number appears at most once; smallest unused number is appended to first row if possible. Sequence gives row 1.
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8
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1, 2, 4, 7, 8, 10, 12, 13, 14, 16, 19, 20, 21, 23, 28, 31, 32, 34, 36, 37, 38, 43, 45, 46, 48, 49, 50, 53, 54, 55, 56, 58, 60, 61, 62, 64, 67, 68, 69, 71, 76, 77, 78, 79, 82, 83, 84, 86, 87, 89, 92, 96, 98, 100, 101, 102, 104, 105, 106, 108, 113, 115
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
| Array begins
1 2 4 7 8 10 12 ...
.3 6 11 15 18 ...
. 9 17 26 33 ...
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MAPLE
| a := [1, 2, 4]; an := 3; b := [3, 6]; bn := 2; c := [9]; cn := 1; h := array(1..10000); h[1] := 1; h[2] := 1; h[3] := 1; h[4] := 1; h[6] := 1; h[9] := 1; m := []; k := 5;
for i from 1 to 200 do for n from k to k+100 do n1 := a[an]+n; n2 := b[bn]+n1; if h[n]<>1 and h[n1]<>1 and h[n2]<>1 then h[n] := 1; h[n1] := 1; h[n2] := 1; an := an+1; bn := bn+1; cn := cn+1; a := [op(a), n]; b := [op(b), n1]; c := [op(c), n2]; k := n+1; break;
else if h[n]<>1 then m := [op(m), n]; fi; fi; od; od; a; b; c; m;
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PROG
| (Haskell)
import Data.List (transpose)
a056231 n = ([1, 2] ++ threeRows !! 0) !! (n-1)
a056232 n = ([3] ++ threeRows !! 1) !! (n-1)
a056233 n = threeRows !! 2 !! (n-1)
threeRows = transpose $ f [4..] [1, 2, 3] [2, 1] [3] [] where
f (u:free) used us vs ws
| u `notElem` used &&
v `notElem` used &&
w `notElem` used = [u, v, w] :
f free (w:v:u:used) (u:us) (v:vs) (w:ws)
| otherwise = f free used us vs ws
where v = u + head us; w = v + head vs
-- Reinhard Zumkeller, Oct 18 2011
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CROSSREFS
| Cf. A056232, A056233, A056234. See also A057153, A052474, A057154, A056230.
Sequence in context: A139212 A175282 A127875 * A131346 A047540 A116478
Adjacent sequences: A056228 A056229 A056230 * A056232 A056233 A056234
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), E. M. Rains, Aug 22 2000
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