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

Author

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

Keywords

• nonn
• nice
• easy

Examples

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

Links

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

Crossrefs

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

Programs

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

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 *)