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A132964 Convolution triangle of A006190. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A111418 A113187 A057967 * A171509 A171505 A134283

Adjacent sequences:  A132961 A132962 A132963 * A132965 A132966 A132967

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Nov 24 2007

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)