A202395 Triangle T(n,k), read by rows, given by (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 1, 1, 2, 4, 2, 5, 13, 11, 3, 13, 40, 46, 24, 5, 34, 120, 172, 128, 50, 8, 89, 354, 603, 572, 319, 98, 13, 233, 1031, 2025, 2311, 1651, 733, 187, 21, 610, 2972, 6592, 8740, 7548, 4324, 1600, 348, 34

Offset

0,4

Comments

T(n,n) = Fibonacci(n+1) = A000045(n+1).

Links

Table of n, a(n) for n=0..44.

Formula

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

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001519(n), A081294(n), A180036(n) for x = -1, 0, 1, 2 respectively.

Example

Triangle begins :
1
1, 1
2, 4, 2
5, 13, 11, 3
13, 40, 46, 24, 5
34, 120, 172, 128, 50, 8
89, 354, 603, 572, 319, 98, 13

Crossrefs

Cf. A000045, A001519, A123585, A202389, A202390,

Sequence in context: A011169 A279481 A233131 * A117903 A167685 A268740

Adjacent sequences: A202392 A202393 A202394 * A202396 A202397 A202398

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 18 2011

Status

approved