A242357 Crescendo trapezoidal.

1, 1, 2, 2, 1, 1, 2, 3, 3, 3, 2, 1, 1, 2, 3, 4, 4, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 5, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7

Offset: 1

Author

Reinhard Zumkeller, May 11 2014

Keywords

• nonn

Comments

a(A000326(n)) = a(A143689(n-1)) = 1;

for all n: a(k) = n, A104249(n-1) <= k <= A005448(n).

Examples

			. Initial values
. seen trapezoidal:                                  666666
.                                    55555          5......5
.                       4444        4.....4        4........4
.             333      3....3      3.......3      3..........3
.      22    2...2    2......2    2.........2    2............2
.  1  1..1  1.....1  1........1  1...........1  1..............1 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A004737.

Programs

Haskell

import Data.List (inits)
a242357 n = a242357_list !! (n-1)
a242357_list = concatMap f $ tail $ inits [1..] where
   f us = (init us) ++ (take v [v, v ..]) ++ vs
          where (v:vs) = reverse us

Mathematica

Table[Join[Range[n-1],PadRight[{},n,n],Range[n-1,1,-1]],{n,9}]//Flatten (* Harvey P. Dale, Oct 23 2020 *)