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A181971 Triangle read by rows: T(n,0) = 1, T(n,n) = floor((n+3)/2) and T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n. 10
1, 1, 2, 1, 3, 2, 1, 4, 5, 3, 1, 5, 9, 8, 3, 1, 6, 14, 17, 11, 4, 1, 7, 20, 31, 28, 15, 4, 1, 8, 27, 51, 59, 43, 19, 5, 1, 9, 35, 78, 110, 102, 62, 24, 5, 1, 10, 44, 113, 188, 212, 164, 86, 29, 6, 1, 11, 54, 157, 301, 400, 376, 250, 115, 35, 6, 1, 12, 65 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Another variant of Pascal's triangle;

row sums: A081254; central terms: T(2*n,n) = A128082(n+1);

T(n,0) = 1;

T(n,1) = n + 1 for n > 0;

T(n,2) = A000096(n-1) for n > 1;

T(n,3) = A105163(n-2) for n > 2;

T(n,n-2) = A005744(n-1) for n > 1;

T(n,n-1) = A024206(n) for n > 0;

T(n,n) = A008619(n+1).

LINKS

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened

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

EXAMPLE

The triangle begins:

.  0:                              1

.  1:                           1     2

.  2:                        1     3     2

.  3:                     1     4     5     3

.  4:                  1     5     9     8     3

.  5:               1     6    14    17    11     4

.  6:            1     7    20    31    28    15     4

.  7:         1     8    27    51    59    43    19     5

.  8:      1     9    35    78   110   102    62    24     5

.  9:   1    10    44   113   188   212   164    86    29     6.

PROG

(Haskell)

a181971 n k = a181971_tabl !! n !! k

a181971_row n = a181971_tabl !! n

a181971_tabl = map snd $ iterate f (1, [1]) where

   f (i, row) = (1 - i, zipWith (+) ([0] ++ row) (row ++ [i]))

(PARI) {T(n, k)=if(n==k, (n+3)\2, if(k==0, 1, if(n>k, T(n-1, k-1)+T(n-1, k))))}

for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print("")) \\ Paul D. Hanna, Jul 18 2012

CROSSREFS

Cf. A035317, A007318, A074909.

Sequence in context: A293600 A191395 A183917 * A104741 A167237 A277813

Adjacent sequences:  A181968 A181969 A181970 * A181972 A181973 A181974

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jul 09 2012

STATUS

approved

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Last modified September 19 15:17 EDT 2019. Contains 327198 sequences. (Running on oeis4.)