A051599 Rows of triangle formed using Pascal's rule except begin and end n-th row with (n+1)st prime.

2, 3, 3, 5, 6, 5, 7, 11, 11, 7, 11, 18, 22, 18, 11, 13, 29, 40, 40, 29, 13, 17, 42, 69, 80, 69, 42, 17, 19, 59, 111, 149, 149, 111, 59, 19, 23, 78, 170, 260, 298, 260, 170, 78, 23, 29, 101, 248, 430, 558, 558, 430, 248, 101, 29, 31, 130, 349, 678, 988, 1116, 988, 678, 349, 130, 31

Offset: 0

Author

Asher Auel

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
2;
3,  3;
5,  6,   5;
7,  11,  11,  7;
11, 18,  22,  18,  11;
13, 29,  40,  40,  29,  13;
17, 42,  69,  80,  69,  42,   17;
19, 59,  111, 149, 149, 111,  59,  19;
23, 78,  170, 260, 298, 260,  170, 78,  23;
29, 101, 248, 430, 558, 558,  430, 248, 101, 29;
31, 130, 349, 678, 988, 1116, 988, 678, 349, 130, 31;
		

Links

• Vincenzo Librandi, Rows n = 0..100, flattened
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A001223; A000040 (left and right edges), A053210 (row sums).

Programs

Haskell

a051599 n k = a051599_tabl !! n !! k
a051599_row n = a051599_tabl !! n
a051599_tabl = map fst $ iterate f ([2], a001223_list) where
   f (row, (d:ds)) =  (zipWith (+) ([d] ++ row) (row ++ [d]), ds)
-- Reinhard Zumkeller, Nov 23 2012

Mathematica

t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = Prime[n + 1], m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t (* T. D. Noe, Jul 31 2013 *)

Extensions

Corrected by James Sellers, Dec 15 1999