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A112883 A skew Jacobsthal-Pascal matrix. 1
1, 0, 1, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 7, 11, 0, 0, 0, 3, 16, 21, 0, 0, 0, 1, 12, 41, 43, 0, 0, 0, 0, 4, 34, 94, 85, 0, 0, 0, 0, 1, 18, 99, 219, 171, 0, 0, 0, 0, 0, 5, 60, 261, 492, 341, 0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683, 0, 0, 0, 0, 0, 0, 6, 95, 576, 1692, 2426, 1365, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370).

Modulo 2, this sequence gives A106344. - Philippe Deléham, Dec 18 2008

LINKS

Table of n, a(n) for n=0..82.

FORMULA

From Philippe Deléham: (Start)

G.f.: 1/(1-yx(1-x)-2x^2*y*2);

Number triangle T(n, k) = Sum_{j=0..2k-n} C(n-k+j, n-k)*C(j, 2k-n-j)*2^(2k-n-j);

T(n, k) = A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) + 2*T(n-2, k-2). (End)

EXAMPLE

Rows begin

  1;

  0, 1;

  0, 1, 3;

  0, 0, 2, 5;

  0, 0, 1, 7, 11;

  0, 0, 0, 3, 16, 21;

  0, 0, 0, 1, 12, 41, 43;

  0, 0, 0, 0,  4, 34, 94,  85;

  0, 0, 0, 0,  1, 18, 99, 219, 171;

  0, 0, 0, 0,  0,  5, 60, 261, 492,  341;

  0, 0, 0, 0,  0,  1, 25, 195, 678, 1101, 683;

CROSSREFS

Cf. A111006.

Sequence in context: A108930 A059682 A156548 * A117138 A292255 A095104

Adjacent sequences:  A112880 A112881 A112882 * A112884 A112885 A112886

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 05 2005

STATUS

approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)