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A276986 Numbers n for which there is a permutation p of (1,2,3,...,n) such that k+p(k) is a Catalan number for 1<=k<=n. 1
0, 1, 3, 4, 9, 10, 12, 13, 28, 29, 31, 32, 37, 38, 40, 41, 90, 91, 93, 94, 99, 100, 102, 103, 118, 119, 121, 122, 127, 128, 130, 131, 297, 298, 300, 301, 306, 307, 309, 310, 325, 326, 328, 329, 334, 335, 337, 338, 387, 388, 390, 391, 396, 397, 399, 400, 415, 416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A001453 is a subsequence. - Altug Alkan, Sep 29 2016

n>=1 is in the sequence if and only if there is a Catalan number c such that c/2 <= n < c and c-n-1 is in the sequence. - Robert Israel, Nov 20 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(i) + a(2^n+1-i) = A000108(n+1)-1 for 1<=i<=2^n. - Robert Israel, Nov 20 2016

EXAMPLE

3 is in the sequence because the permutation (1,3,2) added termwise to (1,2,3) yields (2,5,5) and both 2 and 5 are Catalan numbers.

MAPLE

S:= {0}:

for i from 1 to 8 do

  c:= binomial(2*i, i)/(i+1);

  S:= S union map(t -> c - t - 1, S);

od:

sort(convert(S, list)); # Robert Israel, Nov 20 2016

MATHEMATICA

CatalanTo[n0_] :=

Module[{n = n0}, k = 1; L = {};

  While[CatalanNumber[k] <= 2*n, L = {L, CatalanNumber[k]}; k++];

  L = Flatten[L]]

perms[n0_] := Module[{n = n0, S, func, T, T2},

  func[k_] := Cases[CatalanTo[n], x_ /; 1 <= x - k <= n] - k;

  T = Tuples[Table[func[k], {k, 1, n}]];

  T2 = Cases[T, x_ /; Length[Union[x]] == Length[x]];

  Length[T2]]

Select[Range[41], perms[#] > 0 &]

CROSSREFS

Cf. A000108, A073364.

Sequence in context: A005836 A054591 A121153 * A283984 A283985 A275893

Adjacent sequences:  A276983 A276984 A276985 * A276987 A276988 A276989

KEYWORD

nonn

AUTHOR

Gary E. Davis, Sep 24 2016

EXTENSIONS

More terms from Alois P. Heinz, Sep 28 2016

a(23)-a(58) from Robert Israel, Nov 18 2016

STATUS

approved

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Last modified February 18 17:02 EST 2018. Contains 299325 sequences. (Running on oeis4.)