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

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162741 Fibonacci-Pascal triangle; same as Pascal triangle, but beginning another Pascal triangle to the right of each row starting at row 2. 19
1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 4, 3, 2, 1, 1, 1, 4, 7, 7, 5, 3, 2, 1, 1, 1, 5, 11, 14, 12, 8, 5, 3, 2, 1, 1, 1, 6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1, 1, 1, 7, 22, 41, 51, 46, 33, 21, 13, 8, 5, 3, 2, 1, 1, 1, 8, 29, 63, 92, 97, 79, 54, 34, 21, 13, 8, 5, 3, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Intertwined Pascal-triangles;

the first five rows seen as numbers in decimal representation: row(n) = 110*row(n-1) + 1. - corrected by Reinhard Zumkeller, Jul 16 2013

LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

FORMULA

T(n,k)=T(n-1,k-1)+T(n-1,k), T(n,1)=1 and for n>1: T(n,2*n-2)=T(n,2*n-1)=1. - Reinhard Zumkeller, Jul 16 2013

EXAMPLE

.                                           1

.                                       1,  1, 1

.                                   1,  2,  2, 1, 1

.                               1,  3,  4,  3, 2, 1, 1

.                           1,  4,  7,  7,  5, 3, 2, 1, 1

.                       1,  5, 11, 14, 12,  8, 5, 3, 2, 1, 1

.                   1,  6, 16, 25, 26, 20, 13, 8, 5, 3, 2, 1,1

.               1,  7, 22, 41, 51, 46, 33, 21,13, 8, 5, 3, 2,1,1

.           1,  8, 29, 63, 92, 97, 79, 54, 34,21,13, 8, 5, 3,2,1,1

.       1,  9, 37, 92,155,189,176,133, 88, 55,34,21,13, 8, 5,3,2,1,1

.    1,10, 46,129,247,344,365,309,221,143, 89,55,34,21,13, 8,5,3,2,1,1

. 1,11,56,175,376,591,709,674,530,364,232,144,89,55,34,21,13,8,5,3,2,1,1 .

PROG

(Haskell)

a162741 n k = a162741_tabf !! (n-1) !! (k-1)

a162741_row n = a162741_tabf !! (n-1)

a162741_tabf = iterate

   (\row -> zipWith (+) ([0] ++ row ++ [0]) (row ++ [0, 1])) [1]

-- Reinhard Zumkeller, Jul 16 2013

CROSSREFS

Cf. A005408 (row length), A000225 (row sums), A000045 (central terms), A007318, A136431.

Cf. A021113. - Mark Dols, Jul 18 2009

Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A109906, A111006, A114197, A228074.

Sequence in context: A219365 A140751 A259922 * A104320 A242618 A180264

Adjacent sequences:  A162738 A162739 A162740 * A162742 A162743 A162744

KEYWORD

nonn,tabf

AUTHOR

Mark Dols, Jul 12 2009, Jul 19 2009

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 20:12 EDT 2017. Contains 287241 sequences.