A322062 Sums of pairs of consecutive terms of Pascal's triangle read by row.

2, 2, 2, 3, 3, 2, 4, 6, 4, 2, 5, 10, 10, 5, 2, 6, 15, 20, 15, 6, 2, 7, 21, 35, 35, 21, 7, 2, 8, 28, 56, 70, 56, 28, 8, 2, 9, 36, 84, 126, 126, 84, 36, 9, 2, 10, 45, 120, 210, 252, 210, 120, 45, 10, 2, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 2, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1

Offset

0,1

Comments

Sums of pairs of adjacent terms of A007318. - N. J. A. Sloane, Jan 27 2019

Links

Table of n, a(n) for n=0..77.

Formula

T(n, k) = if (k<n, binomial(n, k) + binomial(n, k+1), binomial(n, k) + binomial(n+1, 0)). - Michel Marcus, Nov 25 2018

Example

The 8th term is 6 because it is the sum of the 8th and 9th terms of Pascal's triangle read by row (3 + 3).
Triangle begins:
  2;
  2,  2;
  3,  3,  2;
  4,  6,  4,  2;
  5, 10, 10,  5,  2;
  ...

Mathematica

v = Flatten[Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]]; Most[v] + Rest[v] (* Amiram Eldar, Nov 25 2018 *)

Prog

(PARI) T(n, k) = if (k<n, binomial(n, k) + binomial(n, k+1), binomial(n, k) + binomial(n+1, 0));
tabl(nn) = for (n=0, nn, for(k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Nov 25 2018

Crossrefs

Cf. A007318, A168557.

Sequence in context: A194288 A360058 A194332 * A368460 A350679 A071451

Adjacent sequences: A322059 A322060 A322061 * A322063 A322064 A322065

Keyword

nonn,tabl,easy

Author

Kei Ryan, Nov 25 2018

Status

approved