A202395 - OEIS

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

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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