A119457 - OEIS

%I #8 Dec 01 2021 07:48:13

%S 1,2,2,3,4,3,4,6,6,5,5,8,9,10,8,6,10,12,15,16,13,7,12,15,20,24,26,21,

%T 8,14,18,25,32,39,42,34,9,16,21,30,40,52,63,68,55,10,18,24,35,48,65,

%U 84,102,110,89,11,20,27,40,56,78,105,136,165,178,144,12,22,30,45,64,91,126,170,220,267,288,233

%N Triangle read by rows: T(n,1)=n, T(n,2)=(n-1)*2 for n>1 and T(n,k)=T(n-1,k-1)+T(n-2,k-2) for 2<k<=n.

%C Row sums give A001891; central terms give A023607;

%C T(n,1) = n;

%C T(n,2) = A005843(n-1) for n>1;

%C T(n,3) = A008585(n-2) for n>2;

%C T(n,4) = A008587(n-3) for n>3;

%C T(n,5) = A008590(n-4) for n>4;

%C T(n,6) = A008595(n-5) for n>5;

%C T(n,7) = A008603(n-6) for n>6;

%C T(n,n-6) = A022090(n-5) for n>6;

%C T(n,n-5) = A022089(n-4) for n>5;

%C T(n,n-4) = A022088(n-3) for n>4;

%C T(n,n-3) = A022087(n-2) for n>3;

%C T(n,n-2) = A022086(n-1) for n>2;

%C T(n,n-1) = A006355(n+1) for n>1;

%C T(n,n) = A000045(n+1);

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number</a>

%F T(n,n) = (n+1)-th Fibonacci number, T(n,k) = (n-k+1)*T(k,k) for 1<=k<n.

%t T[n_, 1] := n;

%t T[n_ /; n > 1, 2] := 2 n - 2;

%t T[n_, k_] /; 2 < k <= n := T[n, k] = T[n - 1, k - 1] + T[n - 2, k - 2];

%t Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Dec 01 2021 *)

%K nonn,tabl

%O 1,2

%A _Reinhard Zumkeller_, May 20 2006