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A132964
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Convolution triangle of A006190.
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0
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..54.
Milan Janjić, Words and Linear Recurrences, J. Int. Seq. 21 (2018), #18.1.4.
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FORMULA
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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
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EXAMPLE
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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;
...
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CROSSREFS
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Cf. A006190, A037027, A054456, A112906.
Sequence in context: A340554 A057967 A347258 * A171509 A171505 A134283
Adjacent sequences: A132961 A132962 A132963 * A132965 A132966 A132967
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Nov 24 2007
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STATUS
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approved
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