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A140685 Triangle T(n,k) read by rows: T = 1 if n is odd and k=(n-1)/2; T = 2 otherwise. 4
1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are A042948(n).

The n-th row can also be described as the coefficient [x^k] of the sum of polynomials x^(m-1) placed on the main and secondary diagonal (in X-shaped pattern) of the m-th row of an n X n matrix:

  x^0   0    0    0   ...   0    0   x^0

   0   x^1   0    0   ...   0   x^1   0

   0    0   x^2   0   ...  x^2   0    0

  ...

The details of the crossing in the center of this matrix depend on whether n is even or odd.

Triangle is read by rows as T(1,0); T(2,0), T(2,1); T(3,0), T(3,1), T(3,2); T(4,0), T(4,1), T(4,2), T(4,3); ... - Antti Karttunen, Oct 10 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 rows of the triangle

EXAMPLE

The triangle starts in row n=1 with columns 0 <= k < n as:

  1;

  2, 2;

  2, 1, 2;

  2, 2, 2, 2;

  2, 2, 1, 2, 2;

  2, 2, 2, 2, 2, 2;

  2, 2, 2, 1, 2, 2, 2;

  2, 2, 2, 2, 2, 2, 2, 2;

  2, 2, 2, 2, 1, 2, 2, 2, 2;

  2, 2, 2, 2, 2, 2, 2, 2, 2, 2;

MATHEMATICA

Clear[M, y, x] M[d_, x_, y_] := Sum[Sum[If[n == m, 1, If[n == d - m + 1, 1, 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] Table[CoefficientList[M[d, x, 1], x], {d, 1, 10}]; Flatten[%]

PROG

(Scheme)

(define (A140685 n) (A140685tr (A002024 n) (- (A002260 n) 1)))

(define (A140685tr n k) (if (and (odd? n) (= k (/ (- n 1) 2))) 1 2))

CROSSREFS

Cf. A002024, A002260, A104041.

Sequence in context: A276788 A282625 A026498 * A055666 A251139 A195061

Adjacent sequences:  A140682 A140683 A140684 * A140686 A140687 A140688

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula and Mats Granvik, Jul 11 2008

EXTENSIONS

Definition simplified by the Assoc. Eds. of the OEIS, Oct 12 2010

More terms from Antti Karttunen, Oct 10 2017

STATUS

approved

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Last modified December 2 16:17 EST 2021. Contains 349445 sequences. (Running on oeis4.)