A102035 Carrie's triangle, read by rows, where the terms are generated by the rule: T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-3,k-1) + T(n-3,k), with T(0,0)=1.

1, 1, 1, 1, 3, 1, 2, 6, 5, 1, 3, 11, 15, 7, 1, 4, 20, 36, 28, 9, 1, 6, 35, 78, 85, 45, 11, 1, 9, 59, 159, 221, 166, 66, 13, 1, 13, 98, 309, 522, 509, 287, 91, 15, 1, 19, 161, 579, 1153, 1382, 1018, 456, 120, 17, 1, 28, 261, 1056, 2421, 3444, 3141, 1840, 681, 153, 19, 1, 41, 419

Offset

0,5

Comments

Column 0 forms A000930. Row sums form A077938. This table was created by Carrie Hanna.

Links

Table of n, a(n) for n=0..67.

Formula

G.f.: A(x, y) = 1/(1-(1+y)*x-y*x^2-(1+y)*x^3).

Example

Generated by adding preceding terms in the triangle
at positions that form the letter 'C': T(n,k) =
T(n-3,k-1) + T(n-3,k) +
T(n-2,k-1) +
T(n-1,k-1) + T(n-1,k).
Rows begin:
[1],
[1,1],
[1,3,1],
[2,6,5,1],
[3,11,15,7,1],
[4,20,36,28,9,1],
[6,35,78,85,45,11,1],
[9,59,159,221,166,66,13,1],
[13,98,309,522,509,287,91,15,1],
[19,161,579,1153,1382,1018,456,120,17,1],...

Prog

(PARI) {T(n, k)=if(n<k|k<0, 0, if(n==0, 1, T(n-1, k)+T(n-1, k-1)+T(n-2, k-1)+T(n-3, k-1)+T(n-3, k)))}

Crossrefs

Cf. A000930, A077938.

Sequence in context: A052417 A130509 A171072 * A055179 A360634 A317863

Adjacent sequences: A102032 A102033 A102034 * A102036 A102037 A102038

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 24 2004

Status

approved