A096646 Triangle (read by rows) where the number of row entries increases by steps of 2 and the entries are stacked in a rectangular fashion. The end entries = 1. Rest of entries in the n-th row are the sum of the entries directly above and to the left and right in all previous rows (total of 3*(n-1) entries).

1, 1, 1, 1, 1, 3, 4, 3, 1, 1, 5, 11, 14, 11, 5, 1, 1, 7, 22, 41, 50, 41, 22, 7, 1, 1, 9, 37, 92, 154, 182, 154, 92, 37, 9, 1, 1, 11, 56, 175, 375, 582, 672, 582, 375, 175, 56, 11, 1

Offset

1,6

Comments

The row sums are 1,3, then 2^(2*(n-2)) * 3. (I.e., A002001 a(n) = 3*4^(n-1), n>0; a(0)=1.) The n-th row is the (2n-1)st row of A072405 (Triangle of C(n,k)-C(n-2,k-1)).

Links

Table of n, a(n) for n=1..49.

Formula

G.f.: 1/[(1-z(1+w+w^2))(1-wz)]. Partial sums of trinomial array A027907. - Ralf Stephan, Jan 09 2005

Example

......................1....................
..................1...1...1................
..............1...3...4...3...1............
..........1...5..11..14..11...5...1........
......1...7..22..41..50..41..22...7..1.....
...1..9..37..92.154.182.154..92..37..9..1..
1.11.56.175.375.582.672.582.375.175.56.11.1

Crossrefs

Cf. A002001, A072405.

Sequence in context: A254745 A111028 A201162 * A306234 A290057 A249790

Adjacent sequences: A096643 A096644 A096645 * A096647 A096648 A096649

Keyword

nonn,tabf

Author

Gerald McGarvey, Aug 14 2004

Status

approved