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A113953 A Jacobsthal matrix. 2
1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, 0, 4, 6, 1, 0, 0, 0, 12, 8, 1, 0, 0, 0, 8, 24, 10, 1, 0, 0, 0, 0, 32, 40, 12, 1, 0, 0, 0, 0, 16, 80, 60, 14, 1, 0, 0, 0, 0, 0, 80, 160, 84, 16, 1, 0, 0, 0, 0, 0, 32, 240, 280, 112, 18, 1, 0, 0, 0, 0, 0, 0, 192, 560, 448, 144, 20, 1, 0, 0, 0, 0, 0, 0, 64, 672 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Rows sums are the Jacobsthal numbers A001045(n+1).

Diagonal sums are the Padovan-Jacobsthal numbers A052947.

Inverse is (1,xc(-2x)), c(x) the g.f. of A000108, with general term k*C(2n-k-1,n-k)(-2)^(n - k)/n.

Triangle read by rows given by (0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 01 2013

LINKS

Table of n, a(n) for n=0..85.

FORMULA

G.f.: 1/(1-xy(1+2x)).

Riordan array (1, x(1+2x)).

T(n, k) = 2^(n-k)*binomial(k, n-k).

T(n,k) = A026729(n,k)*2^(n-k) . - Philippe Deléham, Nov 22 2006

T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 01 2013

EXAMPLE

Rows begin

1;

0, 1;

0, 2, 1;

0, 0, 4, 1;

0, 0, 4, 6, 1;

0, 0, 0, 12, 8, 1;

0, 0, 0, 8, 24, 10, 1;

CROSSREFS

A signed version is A110509.

Sequence in context: A320531 A065719 A204387 * A110509 A319574 A204040

Adjacent sequences:  A113950 A113951 A113952 * A113954 A113955 A113956

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 09 2005

STATUS

approved

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)