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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. 8
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; text; internal format)
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-Fran├žois 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

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Last modified May 9 23:39 EDT 2021. Contains 343746 sequences. (Running on oeis4.)