cp's OEIS Frontend

A348595 Triangle read by rows: Number of walks from (0,0) to (3n,3k) on the square lattice with up and right steps where squares (x,y)=(1,1) mod 3 or (x,y)=(2,2) mod 3 are not entered.

%I A348595 #15 Aug 16 2023 08:22:03
%S A348595 1,1,4,1,8,28,1,12,64,212,1,16,116,520,1676,1,20,184,1052,4288,13604,
%T A348595 1,24,268,1872,9316,35784,112380,1,28,368,3044,17976,81708,301440,
%U A348595 940020,1,32,484,4632,31740,167376,713940,2558280,7936620,1,36,616,6700,52336,314932,1531000,6231100,21842560,67494980
%N A348595 Triangle read by rows: Number of walks from (0,0) to (3n,3k) on the square lattice with up and right steps where squares (x,y)=(1,1) mod 3 or (x,y)=(2,2) mod 3 are not entered.
%H A348595 R. J. Mathar, <a href="/A348595/a348595.pdf">Walks of up and right steps in the square lattice with blocked squares</a>
%F A348595 G.f.: (1-u*v)/(1-u-v-3*u*v) .
%e A348595 The array is symmetric; the non-redundant triangular part starts
%e A348595    1
%e A348595    1    4
%e A348595    1    8   28
%e A348595    1   12   64  212
%e A348595    1   16  116  520  1676
%e A348595    1   20  184 1052  4288  13604
%e A348595    1   24  268 1872  9316  35784 112380
%e A348595    1   28  368 3044 17976  81708 301440  940020
%e A348595    1   32  484 4632 31740 167376 713940 2558280 7936620
%p A348595 A348595 := proc(n,k)
%p A348595     g := (1-u*v)/(1-u-v-3*u*v) ;
%p A348595     coeftayl(%,u=0,n) ;
%p A348595     coeftayl(%,v=0,k) ;
%p A348595 end proc:
%p A348595 seq(seq( A348595(n,k),k=0..n),n=0..10) ;
%t A348595 T[n_, k_] := Module[{u, v}, SeriesCoefficient[(1 - u v)/(1 - u - v - 3 u v), {u, 0, n}] // SeriesCoefficient[#, {v, 0, k}]&];
%t A348595 Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Aug 16 2023 *)
%Y A348595 Cf. A085363 (diagonal), A307584 (walks to (3n+1,3k))
%K A348595 nonn,tabl,easy
%O A348595 0,3
%A A348595 _R. J. Mathar_, Jan 26 2022