A117942 -id:A117942 - cp's OEIS frontend

A117592 a(n) = a(3n) = a(3n+1) = a(3n+2)/2 with a(0)=1.

1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 8, 1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 8, 2, 2, 4, 2, 2, 4, 4, 4, 8, 2, 2, 4, 2, 2, 4, 4, 4

Offset: 0

Paul Barry, Apr 05 2006

Row sums of number triangle A117944.
Product of the nonzero digits of (n written in base 3). - Ilya Gutkovskiy, Nov 15 2020
a(n) = 1, 2, 4, 8, 16, 32, 64 iff n is respectively in A005836, A023699, A023700, A023701, A023702, A023703, A023704. - Bernard Schott, Dec 04 2020

Felix Fröhlich, Table of n, a(n) for n = 0..10000 (first 2001 terms from Vincenzo Librandi)

See A338882 for similar sequences.
Cf. A081603 (log_2), A117942 (signed), A117944.
Cf. A005836, A023699, A023700, A023701, A023702, A023703, A023704.

Nest[ Join[#, #, 2#] &, {1}, 5] (* Robert G. Wilson v, Jul 27 2014 *)

a(n) = 1 << hammingweight(digits(n,3)>>1); \\ Kevin Ryde, Nov 15 2020

from gmpy2 import digits
def A117592(n): return 1<Chai Wah Wu, Dec 05 2024

a(n) = a(3n)/a(0) = a(3n+1)/a(1) = a(3n+2)/a(2).
a(n) = abs(A117942(n)).
G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2) * A(x^3). - Ilya Gutkovskiy, Nov 15 2020
a(n) = 2^A081603(n). - Kevin Ryde, Nov 15 2020

a(0) = 1 added to the Name by Bernard Schott, Dec 04 2020

A290094 Restricted growth sequence transform of A290093.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 3, 5, 6, 2, 7, 5, 4, 8, 9, 5, 10, 11, 3, 5, 12, 5, 9, 13, 6, 11, 14, 2, 7, 5, 7, 15, 10, 5, 10, 11, 4, 15, 9, 8, 16, 17, 9, 18, 19, 5, 10, 13, 10, 18, 20, 11, 21, 22, 3, 5, 12, 5, 9, 13, 12, 13, 23, 5, 10, 13, 9, 17, 24, 13, 20, 25, 6, 11, 23, 11, 19, 25, 14, 22, 26, 2, 7, 5, 7, 15, 10, 5, 10, 11, 7, 27, 10, 15, 28, 18, 10, 29, 21, 5, 10, 13

Offset: 0

Antti Karttunen, Jul 26 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..59049

For all i, j: a(i) = a(j) <=> A290093(n) = A290093(n), thus this matches to all the same base-3 (ternary) related sequences as A290093: A006047, A053735, A062756, A081603, A117942, A206424, A227428, A290091, A290092, A290079, and many others.

A117941 Inverse of number triangle A117939.

Original entry on oeis.org

1, -2, 1, -5, 2, 1, -2, 0, 0, 1, 4, -2, 0, -2, 1, 10, -4, -2, -5, 2, 1, -5, 0, 0, 2, 0, 0, 1, 10, -5, 0, -4, 2, 0, -2, 1, 25, -10, -5, -10, 4, 2, -5, 2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, -2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 10, -4, -2, 0, 0, 0, 0, 0, 0, -5, 2, 1, 4, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 1, -8, 4, 0, 4, -2, 0, 0, 0, 0, 4, -2, 0, -2, 1

Offset: 0

Paul Barry, Apr 05 2006

Row sums are A117942.

T(n, k) mod 2 = A117944(n,k).

			Triangle begins
   1;
  -2,   1;
  -5,   2,  1;
  -2,   0,  0,   1;
   4,  -2,  0,  -2, 1;
  10,  -4, -2,  -5, 2, 1;
  -5,   0,  0,   2, 0, 0,  1;
  10,  -5,  0,  -4, 2, 0, -2, 1;
  25, -10, -5, -10, 4, 2, -5, 2, 1;

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. A117939, A117942, A117944.

M[n_, k_]:= M[n, k]= If[k>n, 0, Sum[JacobiSymbol[Binomial[n, j], 3]*JacobiSymbol[Binomial[n-j, k], 3], {j,0,n}], 0];
m:= m= With[{q = 60}, Table[M[n, k], {n,0,q}, {k,0,q}]];
T[n_, k_]:= Inverse[m][[n+1, k+1]];
Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* G. C. Greubel, Oct 29 2021 *)

cp's OEIS Frontend

A117592 a(n) = a(3n) = a(3n+1) = a(3n+2)/2 with a(0)=1.

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A290094 Restricted growth sequence transform of A290093.

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A117941 Inverse of number triangle A117939.

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