A014631 Numbers in order in which they appear in Pascal's triangle.

1, 2, 3, 4, 6, 5, 10, 15, 20, 7, 21, 35, 8, 28, 56, 70, 9, 36, 84, 126, 45, 120, 210, 252, 11, 55, 165, 330, 462, 12, 66, 220, 495, 792, 924, 13, 78, 286, 715, 1287, 1716, 14, 91, 364, 1001, 2002, 3003, 3432, 105, 455, 1365, 5005, 6435, 16, 560, 1820, 4368, 8008, 11440

Offset

1,2

Comments

A permutation of the natural numbers. - Robert G. Wilson v, Jun 12 2014

In Pascal's triangle a(n) occurs the first time in row A265912(n). - Reinhard Zumkeller, Dec 18 2015

Links

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

Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625 [math.CO], 2020-2021.

F. Richman, Combinations and Permutations

Index entries for triangles and arrays related to Pascal's triangle

Index entries for sequences that are permutations of the natural numbers

Mathematica

lst = {1}; t = Flatten[Table[Binomial[n, m], {n, 16}, {m, Floor[n/2]}]]; Do[ If[ !MemberQ[lst, t[[n]]], AppendTo[lst, t[[n]] ]], {n, Length@t}]; lst (* Robert G. Wilson v *)
DeleteDuplicates[Flatten[Table[Binomial[n, m], {n, 20}, {m, 0, Floor[n/2]}]]] (* Harvey P. Dale, Apr 08 2013 *)

Prog

(Haskell)
import Data.List (nub)
a014631 n = a014631_list !! (n-1)
a014631_list = 1 : (nub $ concatMap tail a034868_tabf)
-- Reinhard Zumkeller, Dec 19 2015
(Python)
from itertools import count, islice
def A014631_gen(): # generator of terms
    s, c =(1, ), set()
    for i in count(0):
        for d in s:
            if d not in c:
                yield d
                c.add(d)
        s=(1, )+tuple(s[j]+s[j+1] for j in range(len(s)-1)) + ((s[-1]<<1, ) if i&1 else ())
A014631_list = list(islice(A014631_gen(), 30)) # Chai Wah Wu, Oct 17 2023

Crossrefs

Cf. A034356, A074909, A119629.

Cf. A034868, A119629 (inverse), A265912.

Sequence in context: A257798 A183079 A119629 * A263266 A263268 A257472

Adjacent sequences: A014628 A014629 A014630 * A014632 A014633 A014634

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

Offset changed by Reinhard Zumkeller, Dec 18 2015

Status

approved