cp's OEIS Frontend

A185081 Triangle T(n,k), read by rows, given by (0, 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.

%I A185081 #24 Jan 26 2020 01:05:43
%S A185081 1,0,1,0,1,2,0,2,4,3,0,3,9,10,5,0,5,18,28,22,8,0,8,35,68,74,45,13,0,
%T A185081 13,66,154,210,177,88,21,0,21,122,331,541,574,397,167,34,0,34,222,686,
%U A185081 1302,1656,1446,850,310,55
%N A185081 Triangle T(n,k), read by rows, given by (0, 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.
%C A185081 Row sums: A133494.
%F A185081 Sum_{k=0..n} T(n,k)*x^k = A033999(n), A000007(n), A133494(n) for x = -1, 0, 1 respectively.
%F A185081 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2), for n > 2, T(0,0) = T(1,1) = T(2,1) = 1, T(1,0) = T(2,0) = 0, T(2,2) = 2.
%F A185081 T(n+1,n) = A004798(n), T(n,n) = T(n+1,1) = A000045(n+1).
%F A185081 T(n,k) = A209138(n,k-1) for k >= 1. - _Philippe Deléham_, Apr 11 2012
%F A185081 G.f.: (-1 + x^2*y + x + x^2)/(-1 + x^2*y + x + x^2 + x*y + x^2*y^2). - _R. J. Mathar_, Aug 11 2015
%e A185081 Triangle begins:
%e A185081   1;
%e A185081   0,  1;
%e A185081   0,  1,  2;
%e A185081   0,  2,  4,  3;
%e A185081   0,  3,  9, 10,  5;
%e A185081   0,  5, 18, 28, 22,  8;
%e A185081   0,  8, 35, 68, 74, 45, 13;
%e A185081 From _Philippe Deléham_, Apr 11 2012: (Start)
%e A185081 Triangle in A209138 begins:
%e A185081   1;
%e A185081   1,  2;
%e A185081   2,  4,  3;
%e A185081   3,  9, 10,  5;
%e A185081   5, 18, 28, 22,  8;
%e A185081   8, 35, 68, 74, 45, 13; (End)
%t A185081 nmax = 9; T[n_, n_] := Fibonacci[n+1]; T[_, 0] = 0; T[n_, 1] := Fibonacci[n]; T[n_, k_] /; 1 < k < n := T[n, k] = T[n - 1, k] + T[n - 1, k - 1] + T[n - 2, k] + T[n - 2, k - 1] + T[n - 2, k - 2]; T[_, _] = 0;
%t A185081 Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 20 2017 *)
%Y A185081 Cf. A000007, A000045, A000244, A004798, A033999, A084938, A133494, A209138.
%K A185081 easy,nonn,tabl
%O A185081 0,6
%A A185081 _Philippe Deléham_, Jan 22 2012
%E A185081 Corrected by _Jean-François Alcover_, Jun 20 2017