This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
First few rows of the triangle: 1; 1, 2; 1, 4, 4; 1, 6, 12, 7; 1, 8, 24, 28, 12; 1, 10, 40, 70, 60, 13; 1, 12, 60, 140, 180, 78, 14; ...
Array begins 1 3 9 26 73 194 ... .2 6 17 47 121 ... . 4 11 30 74 ... .. 7 19 44 ... ... 12 25 ... .... 13 ...
a057153 n = a056230_tabl !! (n-1) !! (n-1) -- Reinhard Zumkeller, Nov 19 2011
Array begins 1 3 9 26 73 194 ... .2 6 17 47 121 ... . 4 11 30 74 ... .. 7 19 44 ... ... 12 25 ... .... 13 ...
import Data.List (intersect, union, (\\))
a056230 n k = a056230_tabl !! (n-1) !! (k-1)
a056230_tabl = [1] : f [1] [2..] [1] where
f adiag (a:as) us | null (adiag' `intersect` us) =
adiag' : f adiag' (as \\ adiag') (us `union` adiag')
| otherwise = f adiag as us
where adiag' = scanl (+) a adiag
-- Reinhard Zumkeller, Nov 19 2011
Array begins 1 2 4 7 8 10 12 ... .3 6 11 15 18 ... . 9 17 26 33 ...
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
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;
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 *)
Array begins 1 2 4 7 8 10 12 ... .3 6 11 15 18 ... . 9 17 26 33 ...
cf. A056231.
Array begins 1 2 4 7 8 10 12 ... .3 6 11 15 18 ... . 9 17 26 33 ...
cf. A056231.
Array begins 1 2 4 7 8 10 12 ... .3 6 11 15 18 ... . 9 17 26 33 ...
a056234 n = a056234_list !! (n-1)
a056234_list = notUsed 1 a056231_list a056232_list a056233_list where
notUsed x us'@(u:us) vs'@(v:vs) ws'@(w:ws)
| x == u = notUsed (x + 1) us vs' ws'
| x == v = notUsed (x + 1) us' vs ws'
| x == w = notUsed (x + 1) us' vs' ws
| otherwise = x : notUsed (x + 1) us' vs' ws'
-- Reinhard Zumkeller, Nov 07 2011
Array begins 1 3 9 26 73 194 ... .2 6 17 47 121 ... . 4 11 30 74 ... .. 7 19 44 ... ... 12 25 ... .... 13 ...
import Data.List (intersect, union, (\\))
a057154 n = a057154_list !! (n-1)
a057154_list = g [1] [2..] [1] where
g ds (a:as) us
| null (ds' `intersect` us) = g ds' (as \\ ds') (us `union` ds')
| otherwise = a : g ds as us
where ds' = scanl (+) a ds
-- Reinhard Zumkeller, Nov 19 2011
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