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A060556 Bisection of triangle A060098: odd indexed members of column sequences of A060098 (not counting leading zeros). 5
1, 1, 2, 1, 6, 3, 1, 12, 16, 4, 1, 20, 50, 32, 5, 1, 30, 120, 140, 55, 6, 1, 42, 245, 448, 316, 86, 7, 1, 56, 448, 1176, 1284, 622, 126, 8, 1, 72, 756, 2688, 4170, 3102, 1113, 176, 9, 1, 90, 1200, 5544, 11550, 12122 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums give A060557. Column sequences without leading zeros give for m=0..5: A000012 (powers of 1), A002378 = 2*A000217, A004320, 4*A040977, A060558, 2*A060559.

Companion triangle (even indexed members) A060102.

With offset 1 for n and k, T(n,k) is the number of (1-2-3)-avoiding trapezoidal words of length n that contain n+1-k 1s. A trapezoidal word (following Riordan) is a sequence (a_1,a_2,...,a_n) of integers with 1<=a_i<=2i-1. For example, T(3,3)=3 counts 122, 132, 133 and T(4,2)=12 counts 1112, 1113, 1114, 1115, 1116, 1117, 1121, 1131, 1141, 1151, 1211, 1311. [From David Callan, Aug 25 2009]

LINKS

Table of n, a(n) for n=0..50.

FORMULA

a(n, m)= A060098(2*n+1-m, m).

G.f. for column m: (x^m)*Po(m+1, x)/(1-x)^(2*m+1), with Po(n, x)=sum(binomial (n, 2*j+1)*x^j, j=0..floor(n/2)) (odd members of row n of Pascal triangle A007318).

a(n, m)= sum(binomial(n-j+m, 2*m)*binomial(m+1, 2*j+1), j=0..floor((m+1)/2)), n >= m >= 0, else zero.

EXAMPLE

{1}; {1,2}; {1,6,3}; {1,12,16,4}; ...; Po(3,x)=3+x.

CROSSREFS

Sequence in context: A016545 A142977 A120108 * A222969 A132813 A034898

Adjacent sequences:  A060553 A060554 A060555 * A060557 A060558 A060559

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 06 2001

STATUS

approved

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Last modified November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)