%I A111808
%S A111808 1,1,1,1,2,3,1,3,6,7,1,4,10,16,19,1,5,15,30,45,51,1,6,21,50,90,126,141,
%T A111808 1,7,28,77,161,266,357,393,1,8,36,112,266,504,784,1016,1107,1,9,45,156,
%U A111808 414,882,1554,2304,2907,3139,1,10,55,210,615,1452,2850,4740,6765,8350
%N A111808 Left half of trinomial triangle (A027907), triangle read by rows.
%C A111808 Consider a doubly infinite chessboard with squares labeled (i,j), i in 
               Z, j in Z; number of king-paths of length j from (0,0) to (i,j), 
               0 <= i <= j, is T(j,i-j). - Harrie Grondijs (hgrondijs(AT)epo.org), 
               May 27 2005. Cf. A026300, A114929, A114972.
%D A111808 Harrie Grondijs, Neverending Quest of Type C, Volume B - the endgame 
               study-as-struggle.
%H A111808 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrinomialTriangle.html">Trinomial Triangle</a>
%H A111808 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrinomialCoefficient.html">Trinomial Coefficient</a>
%F A111808 (1 + x + x^2)^n = Sum(T(n,k)*x^k: 0<=k<=n) + Sum(T(n,k)*x^(2*n-k): 0<=k<n);
%F A111808 T(n, k) = A027907(n, k) = Sum(binomial(n, n-k+2*i) * binomial(n-k+2*i, 
               i): 0<=i<k/2), 0<=k<=n.
%Y A111808 Row sums give A027914; central terms give A027908;
%Y A111808 T(n, 0)=0; T(n, 1)=n for n>1; T(n, 2)=A000217(n) for n>1;
%Y A111808 T(n, 3) = A005581(n) for n>2;
%Y A111808 T(n, 4) = A005712(n) for n>3;
%Y A111808 T(n, 5) = A000574(n) for n>4;
%Y A111808 T(n, 6) = A005714(n) for n>5;
%Y A111808 T(n, 7) = A005715(n) for n>6;
%Y A111808 T(n, 8) = A005716(n) for n>7;
%Y A111808 T(n, 9) = A064054(n-5) for n>8;
%Y A111808 T(n, n-5) = A098470(n) for n>4;
%Y A111808 T(n, n-4) = A014533(n-3) for n>3;
%Y A111808 T(n, n-3) = A014532(n-2) for n>2;
%Y A111808 T(n, n-2) = A014531(n-1) for n>1;
%Y A111808 T(n, n-1) = A005717(n) for n>0;
%Y A111808 T(n, n) = central terms of A027907 = A002426(n).
%Y A111808 Sequence in context: A118981 A117938 A101912 this_sequence A081422 A027555 
               A059481
%Y A111808 Adjacent sequences: A111805 A111806 A111807 this_sequence A111809 A111810 
               A111811
%K A111808 nonn,tabl
%O A111808 1,5
%A A111808 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2005