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A117898 Number triangle 2^abs(L(C(n,2)/3) - L(C(k,2)/3))*[k<=n] where L(j/p) is the Legendre symbol of j and p. 5
1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are A117899. Diagonal sums are A117900. Inverse is A117901. A117898 mod 2 is A117904.

LINKS

G. C. Greubel, Table of n, a(n) for the first 101 rows, flattened

FORMULA

G.f.: (1 +x*(1+y) +x^2*(2+2*y+y^2) +x^3*y(1+2*y) +2*x^4*y^2)/((1-x^3)*(1-x^3*y^3)).

T(n, k) = [k<=n]*2^abs(L(C(n,2)/3) - L(C(k,2)/3)).

EXAMPLE

Triangle begins

  1;

  1, 1;

  2, 2, 1;

  1, 1, 2, 1;

  1, 1, 2, 1, 1;

  2, 2, 1, 2, 2, 1;

  1, 1, 2, 1, 1, 2, 1;

  1, 1, 2, 1, 1, 2, 1, 1;

  2, 2, 1, 2, 2, 1, 2, 2, 1;

  1, 1, 2, 1, 1, 2, 1, 1, 2, 1;

  1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1;

  2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1;

  1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1;

MATHEMATICA

Flatten[CoefficientList[CoefficientList[Series[(1 +x(1+y) +x^2(2+2y+y^2) +x^3*y(1 +2y) +2x^4*y^2)/((1-x^3)(1-x^3*y^3)), {x, 0, 15}, {y, 0, 15}], x], y]] (* G. C. Greubel, May 03 2017 *)

T[n_, k_]:= 2^Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Sep 27 2021 *)

PROG

(Sage)

def T(n, k): return 2^abs(kronecker(binomial(n, 2), 3) - kronecker(binomial(k, 2), 3))

flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Sep 27 2021

CROSSREFS

Cf. A117898, A117899, A117900, A117901, A117904.

Sequence in context: A239110 A278514 A243840 * A212810 A072344 A140500

Adjacent sequences:  A117895 A117896 A117897 * A117899 A117900 A117901

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Apr 01 2006

STATUS

approved

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Last modified August 10 12:45 EDT 2022. Contains 356039 sequences. (Running on oeis4.)