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A134658 Triangle read by rows, giving coefficients of extended Jacobsthal recurrence. 3
3, 1, 2, 2, -1, 2, 3, -3, 1, 2, 4, -6, 4, -1, 2, 5, -10, 10, -5, 1, 2, 6, -15, 20, -15, 6, -1, 2, 7, -21, 35, -35, 21, -7, 1, 2, 8, -28, 56, -70, 56, -28, 8, -1, 2, 9, -36, 84, -126, 126, -84, 36, -9, 1, 2, 10, -45, 120, -210, 252, -210, 120, -45, 10, -1, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sequence identical to half its p-th differences from the second term.

This sequence is the second of a family after A135356.

This triangle looks like a Pascal's triangle without first column, and with signs and with additional right diagonal consisting of 2's. - Michel Marcus, Apr 07 2019

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Every row sums to 3. - Jean-François Alcover, Apr 04 2019 (further to a remark e-mailed by Paul Curtz).

EXAMPLE

Triangle begins

3;                : A000244 = 1, 3, 9, 27, ... is the main sequence

1, 2;             : A001045 = 0, 1, 1, 3, ... is the main sequence

2, -1, 2;         : 0, 0, (A007910 = 1, 2, 3, ... ) is the main sequence

3, -3, 1, 2;      : 0, 0, 0, 1, 3, 6, 10, 17, ... is the main sequence

4, -6, 4, -1, 2;  : A134987 = 0, 0, 0, 0, 1, ... is the main sequence

...

See signatures of linear recurrence of corresponding sequences.

MATHEMATICA

T[n_, k_] := T[n, k] = Which[n == 0, 3, k == n, 2, k == 0, n, k == n-1, (-1)^k, True, T[n-1, k] - T[n-1, k-1]];

Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 06 2019 *)

CROSSREFS

Cf. A000244, A001045, A007910, A134977 (sum of antidiagonals), A134987, A135356.

Sequence in context: A087282 A105973 A088429 * A296518 A111951 A222593

Adjacent sequences:  A134655 A134656 A134657 * A134659 A134660 A134661

KEYWORD

sign,tabl

AUTHOR

Paul Curtz, Feb 01 2008

EXTENSIONS

In agreement with author, T(0, 0) = 3 and offset 0 by Michel Marcus, Apr 06 2019

STATUS

approved

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)