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

1,3

Comments

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

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

Links

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

Example

. 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 .

Mathematica

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

Prog

(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

Crossrefs

Cf. A004737.

Sequence in context: A156282 A203776 A343559 * A120423 A113137 A220603

Adjacent sequences: A242354 A242355 A242356 * A242358 A242359 A242360

Keyword

nonn

Author

Reinhard Zumkeller, May 11 2014

Status

approved