login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A092689 Triangle, read by rows, such that the convolution of each row with {1,2} produces a triangle which, after the main diagonal is divided by 2 and the triangle is flattened, equals this flattened form of the original triangle. 7
1, 1, 1, 3, 1, 3, 7, 5, 3, 7, 19, 13, 13, 7, 19, 51, 39, 33, 33, 19, 51, 141, 111, 99, 85, 89, 51, 141, 393, 321, 283, 259, 229, 243, 141, 393, 1107, 925, 825, 747, 701, 627, 675, 393, 1107, 3139, 2675, 2397, 2195, 2029, 1929, 1743, 1893, 1107, 3139, 8953, 7747 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

First column and main diagonal forms the central trinomial coefficients (A002426). Row sums form A092690.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

T(n, k) = 2*T(n-1, k) + T(n-1, k+1) for 0<k<n, with T(n, n)=T(n, 0)=T(n+1, n)=A002426(n), T(0, 0)=1, T(0, 1)=T(1, 0)=1.

EXAMPLE

Rows begin:

{1},

{1,1},

{3,1,3},

{7,5,3,7},

{19,13,13,7,19},

{51,39,33,33,19,51},

{141,111,99,85,89,51,141},

{393,321,283,259,229,243,141,393},

{1107,925,825,747,701,627,675,393,1107},

{3139,2675,2397,2195,2029,1929,1743,1893,1107,3139},

{8953,7747,6989,6419,5987,5601,5379,4893,5353,3139,8953},...

Convolution of each row with {1,2} forms the triangle:

{1,2},

{1,3,2},

{3,7,5,6},

{7,19,13,13,14},

{19,51,39,33,33,38},

{51,141,111,99,85,89,102},

{141,393,321,283,259,229,243,282},...

which, after the main diagonal is divided by 2 and the triangle is flattened, equals the original triangle in flattened form: {1,1,1,3,1,3,7,5,3,7,19,...}.

PROG

(PARI) T(n, k)=if(n<0 || k>n, 0, if(n==0 && k==0, 1, if(n==1 && k<=1, 1, if(k==n-1, T(n-1, 0), if(k==n, T(n, 0), 2*T(n-1, k)+T(n-1, k+1))))))

CROSSREFS

Cf. A002426, A092683, A092686, A092690.

Sequence in context: A107461 A035619 A280995 * A281553 A064434 A086401

Adjacent sequences:  A092686 A092687 A092688 * A092690 A092691 A092692

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Mar 04 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)