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A279006 Alternating Jacobsthal triangle read by rows (second version). 3
1, 1, 1, 1, 0, 1, 1, -1, 1, 1, 1, -2, 2, 0, 1, 1, -3, 4, -2, 1, 1, 1, -4, 7, -6, 3, 0, 1, 1, -5, 11, -13, 9, -3, 1, 1, 1, -6, 16, -24, 22, -12, 4, 0, 1, 1, -7, 22, -40, 46, -34, 16, -4, 1, 1, 1, -8, 29, -62, 86, -80, 50, -20, 5, 0, 1, 1, -9, 37, -91, 148, -166, 130, -70, 25, -5, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..77.

Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.

FORMULA

T(i, j) = A220074(i, i-j). See (3.7) in arxiv link. - Michel Marcus, Jun 17 2017

EXAMPLE

Triangle begins:

  1,

  1,   1,

  1,   0,   1,

  1,  -1,   1,   1,

  1,  -2,   2,   0,   1,

  1,  -3,   4,  -2,   1,   1,

  1,  -4,   7,  -6,   3,   0,   1,

  1,  -5,  11, -13,   9,  -3,   1,   1,

  1,  -6,  16, -24,  22, -12,   4,   0,   1,

  ...

MATHEMATICA

T[i_, i_] = T[_, 0] = 1; T[i_, j_] := T[i, j] = T[i-1, j] - T[i-1, j-1];

Table[T[i, j], {i, 0, 11}, {j, 0, i}] // Flatten (* Jean-Fran├žois Alcover, Sep 06 2018 *)

PROG

(PARI) \\ using arxiv (3.1) and (3.7) formulas where A is A220074 and B is this sequence

A(i, j) = if ((i < 0), 0, if (j==0, 1, A(i - 1, j - 1) - A(i - 1, j))); \\ A220074

B(i, j) = A(i, i-j);

tabl(nn) = for (i=0, nn, for (j=0, i, print1(B(i, j), ", ")); print()); \\ Michel Marcus, Jun 17 2017

CROSSREFS

See A112468, A112555 and A108561 for other versions.

Columns give A000124, A003600, A223718, A257890, A223659.

Sequence in context: A112185 A192062 A172371 * A112555 A108561 A174626

Adjacent sequences:  A279003 A279004 A279005 * A279007 A279008 A279009

KEYWORD

sign,tabl

AUTHOR

N. J. A. Sloane, Dec 07 2016

EXTENSIONS

More terms from Michel Marcus, Jun 17 2017

STATUS

approved

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Last modified June 18 17:05 EDT 2019. Contains 324214 sequences. (Running on oeis4.)