A056231 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.

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

Offset

1,2

Links

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

Example

Array begins
1 2 4 7 8 10 12 ...
.3 6 11 15 18 ...
. 9 17 26 33 ...

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;

Mathematica

a = {1, 2, 4}; an = 3; b = {3, 6}; bn = 2; c = {9}; cn = 1; Clear[h]; h[_] = 0; h[1] = h[2] = h[3] = h[4] = h[6] = h[9] = 1; m = {}; k = 5;
For[i = 1, i <= 200, i++, For[n = k, n <= k + 100, n++, n1 = a[[an]] + n; n2 = b[[bn]] + n1; If[h[n] != 1 && h[n1] != 1 && h[n2] != 1, h[n] = 1; h[n1] = 1; h[n2] = 1; an++; bn++; cn++; AppendTo[a, n]; AppendTo[b, n1]; AppendTo[c, n2]; k = n+1; Break[], If[h[n] != 1, AppendTo[m, n]]]]];
{a, b, c, m} (* Jean-François Alcover, Dec 17 2019, translated from Maple *)

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

Crossrefs

Cf. A056232, A056233, A056234. See also A057153, A052474, A057154, A056230.

Sequence in context: A139212 A175282 A127875 * A248637 A131346 A341350

Adjacent sequences: A056228 A056229 A056230 * A056232 A056233 A056234

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, E. M. Rains, Aug 22 2000

Status

approved