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A275326 Triangle read by rows, T(n,k) = ceiling(A275325(n,k)/2) for n>=0 and 0<=k<=n. 1
1, 0, 1, 0, 1, 0, 3, 0, 2, 1, 0, 10, 5, 0, 5, 4, 1, 0, 35, 28, 7, 0, 14, 14, 6, 1, 0, 126, 126, 54, 9, 0, 42, 48, 27, 8, 1, 0, 462, 528, 297, 88, 11, 0, 132, 165, 110, 44, 10, 1, 0, 1716, 2145, 1430, 572, 130, 13, 0, 429, 572, 429, 208, 65, 12, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

An extension of the Catalan triangle A128899.

LINKS

Table of n, a(n) for n=0..64.

Peter Luschny, Orbitals

FORMULA

T(n,k) = A275325(n,k)/2 for n>=2.

T(n,1) = A057977(n) for n>=1 (the extended Catalan numbers).

For odd n: T(n,1) = Sum_{k>=0} T(n+1,k).

Main diagonal: T(n, floor(n/2)) = A093178(n).

EXAMPLE

Triangle starts:

[ n] [k=0,1,2,...] [row sum]

[ 0] [1] 1

[ 1] [0, 1] 1

[ 2] [0, 1] 1

[ 3] [0, 3] 3

[ 4] [0, 2, 1] 3

[ 5] [0, 10, 5] 15

[ 6] [0, 5, 4, 1] 10

[ 7] [0, 35, 28, 7] 70

[ 8] [0, 14, 14, 6, 1] 35

[ 9] [0, 126, 126, 54,  9] 315

[10] [0, 42, 48, 27, 8, 1] 126

[11] [0, 462, 528, 297, 88, 11] 1386

[12] [0, 132, 165, 110, 44, 10, 1] 462

PROG

(Sage)

# Function orbital_factors is in A275325.

def half_orbital_factors(n):

    F = orbital_factors(n)

    return [f//2 for f in F] if n >= 2 else F

for n in (0..12): print half_orbital_factors(n)

CROSSREFS

Cf. A057977, A093178, A128899, A275324 (row sums), A275325.

Sequence in context: A291786 A004603 A174951 * A092926 A052311 A181786

Adjacent sequences:  A275323 A275324 A275325 * A275327 A275328 A275329

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, Aug 15 2016

STATUS

approved

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)