A117317 Triangle related to partitions of n.

1, 2, 1, 4, 5, 1, 8, 16, 9, 1, 16, 44, 41, 14, 1, 32, 112, 146, 85, 20, 1, 64, 272, 456, 377, 155, 27, 1, 128, 640, 1312, 1408, 833, 259, 35, 1, 256, 1472, 3568, 4712, 3649, 1652, 406, 44, 1, 512, 3328, 9312, 14608, 14002, 8361, 3024, 606, 54, 1, 1024, 7424, 23552

Offset

0,2

Comments

Row sums are A007052. Diagonal sums are A052988. Reversal of A056242.

Essentially given by (0, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 28 2012

Links

Reinhard Zumkeller, Rows n = 0..125 of table, flattened

Formula

Number triangle T(n,k)=sum{j=0..n-k, C(n+j,k)C(n-k,j)}

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k-1) - T(n-2,k-2) for n>1. - Philippe Deléham, Jan 28 2012

G.f.: (1-y*x)/(1-2*(y+1)*x+y*(y+1)*x^2). - Philippe Deléham, Jan 28 2012

Example

Triangle begins
1,
2, 1,
4, 5, 1,
8, 16, 9, 1,
16, 44, 41, 14, 1,
32, 112, 146, 85, 20, 1,
64, 272, 456, 377, 155, 27, 1
Triangle (0, 2, 0, 0, 0, 0, ...) DELTA (1, 0, 1/2, 1/2, 0, 0, ...) begins :
1
0, 1
0, 2, 1
0, 4, 5, 1
0, 8, 16, 9, 1
0, 16, 44, 41, 14, 1
0, 32, 112, 146, 85, 20, 1
0, 64, 272, 456, 377, 155, 27, 1

Prog

(Haskell)
a117317 n k = a117317_tabl !! n !! k
a117317_row n = a117317_tabl !! n
a117317_tabl = map reverse a056242_tabl
-- Reinhard Zumkeller, May 08 2014

Crossrefs

Cf. Columns : A000079, A053220, A056243 ; Diagonals : A000012, A000096

Sequence in context: A362926 A102661 A121574 * A124237 A123876 A114164

Adjacent sequences: A117314 A117315 A117316 * A117318 A117319 A117320

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 07 2006

Status

approved