A124790 -id:A124790

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A124791

Row sums of number triangle A124790.

+20
2

1, 1, 1, 3, 5, 13, 29, 73, 181, 465, 1205, 3171, 8425, 22597, 61073, 166195, 454949, 1251985, 3461573, 9611191, 26787377, 74916661, 210178457, 591347989, 1668172841, 4717282753, 13369522249, 37970114703, 108045430901

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Row sums of a generalized Motzkin triangle.

Apparently the Motzkin transform of A105811, after the sign of A105811(1) is negated. - R. J. Mathar, Dec 11 2008

Hankel transform is A159964. - Paul Barry, Apr 28 2009

LINKS

Table of n, a(n) for n=0..28.

FORMULA

Conjecture: (n+1)*a(n) +(-n+2)*a(n-1) +(-5*n+7)*a(n-2) +3*(-n+2)*a(n-3) = 0. - R. J. Mathar, Dec 02 2014

CROSSREFS

Cf. A105811, A124790, A159964.

KEYWORD

nonn

AUTHOR

Paul Barry, Nov 07 2006

STATUS

approved

A124816

Product of Riordan array (1,x(1-x^2))^(-1) and number triangle T(n,k)=C(floor(k/2),n-k).

+10
2

1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 0, 3, 3, 3, 2, 1, 0, 0, 7, 4, 5, 2, 1, 0, 12, 12, 12, 10, 6, 3, 1, 0, 0, 30, 18, 24, 12, 9, 3, 1, 0, 55, 55, 55, 50, 32, 22, 10, 4, 1, 0, 0, 143, 88, 121, 66, 57, 25, 14, 4, 1, 0, 273, 273, 273

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,13

COMMENTS

Product of A124305 and A124788. Columns include aerated A001764,A047749(n+1),A124817,A084081. Row sums are A124818.

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

Triangle begins

0, 1,

0, 0, 1,

0, 1, 1, 1,

0, 0, 2, 1, 1,

0, 3, 3, 3, 2, 1,

0, 0, 7, 4, 5, 2, 1,

0, 12, 12, 12, 10, 6, 3, 1,

0, 0, 30, 18, 24, 12, 9, 3, 1,

0, 55, 55, 55, 50, 32, 22, 10, 4, 1

CROSSREFS

Cf. A124790.

KEYWORD

nonn,tabl

AUTHOR

Paul Barry, Nov 08 2006

STATUS

approved

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