A362379 Convolution triangle of A052547(n).

1, 0, 1, 2, 0, 1, 1, 4, 0, 1, 5, 2, 6, 0, 1, 5, 14, 3, 8, 0, 1, 14, 14, 27, 4, 10, 0, 1, 19, 49, 27, 44, 5, 12, 0, 1, 42, 68, 113, 44, 65, 6, 14, 0, 1, 66, 175, 159, 214, 65, 90, 7, 16, 0, 1, 131, 286, 465, 304, 360, 90, 119, 8, 18, 0, 1

Offset

0,4

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k) - T(n-2,k-1) - T(n-3,k) ; T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = T(2,1) = 0, T(2,0) = 2, T(n,k) = 0 if k<0 or if k>n .

Sum_{k = 0..n} T(n,k)*x^k = A052547(n), A077998(n), A052536(n), A052941(n) for x = 0, 1, 2, 3 respectively.

Sum_{k = 0..n} T(n,k)*2^(n-k) = A139818(n+1) = A001045(n+1)^2.

Example

Triangle begins, for n>=0, 0<=k<=n :
   1 ;
   0,  1 ;
   2,  0,   1 ;
   1,  4,   0,  1 ;
   5,  2,   6,  0,  1 ;
   5, 14,   3,  8,  0,  1 ;
  14, 14,  27,  4, 10,  0,  1 ;
  19, 49,  27, 44,  5, 12,  0, 1 ;
  42, 68, 113, 44, 65,  6, 14, 0, 1 ;
  ...

Crossrefs

Cf. A052547, A077998 (row sums), A052964 (diagonal sums).

Sequence in context: A221755 A354666 A110298 * A144740 A283272 A292166

Adjacent sequences: A362376 A362377 A362378 * A362380 A362381 A362382

Keyword

nonn,easy,tabl

Author

Philippe Deléham, Apr 20 2023

Status

approved