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A112899 A skew Pell-Pascal triangle. 2
1, 0, 2, 0, 1, 5, 0, 0, 4, 12, 0, 0, 1, 14, 29, 0, 0, 0, 6, 44, 70, 0, 0, 0, 1, 27, 131, 169, 0, 0, 0, 0, 8, 104, 376, 408, 0, 0, 0, 0, 1, 44, 366, 1052, 985, 0, 0, 0, 0, 0, 10, 200, 1212, 2888, 2378, 0, 0, 0, 0, 0, 1, 65, 810, 3842, 7813, 5741, 0, 0, 0, 0, 0, 0, 12, 340, 3032, 11784 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Main diagonal is A000129. Row sums are A002605. Column sums are A006190(n+1).

A skewed version of the Riordan array (1/(1-2x-x^2),x/(1-2x-x^2)), see A054456 . - Philippe Deléham, Nov 21 2007

Triangle, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,...] DELTA [2,1/2,-1/2,0,0,0,0,0,...] where DELTA is the operator defined in A084938. [From Philippe Deléham, Jan 30 2010]

LINKS

Table of n, a(n) for n=0..75.

FORMULA

G.f.: 1/(1-2xy(1+x/2)-x^2*y^2); T(n, k)=sum{j=0..floor((2k-n)/2), C(k-j, n-k)C(2k-n, j)2^(2k-2j-n)}; T(n, k) = 2*T(n-1, k-1) + T(n-2, k-1) +T(n-2, k-2).

EXAMPLE

Rows begin

1;

0, 2;

0, 1, 5;

0, 0, 4, 12;

0, 0, 1, 14, 29;

0, 0, 0, 6, 44, 70;

0, 0, 0, 1, 27, 131, 169;

0, 0, 0, 0, 8, 104, 376, 408;

CROSSREFS

Cf. A111006, A112906 [From Philippe Deléham, Jan 30 2010]

Sequence in context: A244128 A016584 A293961 * A212808 A209687 A108263

Adjacent sequences:  A112896 A112897 A112898 * A112900 A112901 A112902

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 05 2005

STATUS

approved

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Last modified December 11 07:18 EST 2019. Contains 329914 sequences. (Running on oeis4.)