A132964 Convolution triangle of A006190.

1, 3, 1, 10, 6, 1, 33, 29, 9, 1, 109, 126, 57, 12, 1, 360, 516, 306, 94, 15, 1, 1189, 2034, 1491, 600, 140, 18, 1, 3927, 7807, 6813, 3385, 1035, 195, 21, 1, 12970, 29382, 29737, 17568, 6630, 1638, 259, 24, 1, 42837, 108923, 125406, 85826, 38493, 11739, 2436, 332, 27, 1

Offset

0,2

Comments

As a Riordan array, this is (1/(1-3x-x^2),x/(1-3x-x^2)).

T(n,k) is the number of words of length n over {0,1,2,3,4} having k letters 4 and avoiding runs of odd length for the letter 0. - Milan Janjic, Jan 14 2017

Links

Table of n, a(n) for n=0..54.

Milan Janjić, Words and Linear Recurrences, J. Int. Seq. 21 (2018), #18.1.4.

Formula

Sum_{k=0..n} T(n,k) = A001076(n+1).

Sum_{k=0..floor(n/2)} T(n-k,k) = A007482(n).

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) + T(n-2,k), T(0,0)=1, T(n,k)=0 if k<0 or k>n. - Philippe Deléham, Dec 08 2013

Example

Triangle begins:
      1;
      3,      1;
     10,      6,      1;
     33,     29,      9,     1;
    109,    126,     57,    12,     1;
    360,    516,    306,    94,    15,     1;
   1189,   2034,   1491,   600,   140,    18,    1;
   3927,   7807,   6813,  3385,  1035,   195,   21,   1;
  12970,  29382,  29737, 17568,  6630,  1638,  259,  24,  1;
  42837, 108923, 125406, 85826, 38493, 11739, 2436, 332, 27, 1;
  ...

Crossrefs

Cf. A006190, A037027, A054456, A112906.

Sequence in context: A340554 A057967 A347258 * A171509 A171505 A134283

Adjacent sequences: A132961 A132962 A132963 * A132965 A132966 A132967

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Nov 24 2007

Status

approved