A152602 - OEIS

%I #15 Feb 03 2025 02:22:59

%S 1,1,1,1,6,1,1,16,16,1,1,36,76,36,1,1,76,256,256,76,1,1,156,736,1176,

%T 736,156,1,1,316,1936,4336,4336,1936,316,1,1,636,4816,14016,19696,

%U 14016,4816,636,1,1,1276,11536,41536,76096,76096,41536,11536,1276,1,1,2556

%N a(n) = 2*{0,a(n-2),0} + 2*{-1/2,a(n-1)}+2*{a(n-1),-1/2}.

%F a(n) = 2*{0,a(n-2),0}+2*{-1/2,a(n-1)}+2*{a(n-1),-1/2}.

%F T(n,k) = 2*T(n-2,k-1)+2*T(n-1,k-1)+2*T(n-1,k), 0<k<n, n>1. T(n,0) = 2*T(n-1,0)-1, n>1. T(n,n) = 2*T(n-1,n-1)-1, n>1. Row sum recurrence: s(n) = 5*s(n-1)-2*s(n-2)-2*s(n-3), s = Sum_{k=0..n} T(n,k). - _R. J. Mathar_, Dec 10 2008

%e Triangle begins:

%e   {1},

%e   {1, 1},

%e   {1, 6, 1},

%e   {1, 16, 16, 1},

%e   {1, 36, 76, 36, 1},

%e   {1, 76, 256, 256, 76, 1},

%e   {1, 156, 736, 1176, 736, 156, 1},

%e   {1, 316, 1936, 4336, 4336, 1936, 316, 1},

%e   {1, 636, 4816, 14016, 19696, 14016, 4816, 636, 1},

%e   {1, 1276, 11536, 41536, 76096, 76096, 41536, 11536, 1276, 1},

%e   {1, 2556, 26896, 115776, 263296, 343776, 263296, 115776, 26896, 2556, 1},

%e   ...

%t a[1] = {1, 1};

%t a[n_] := a[n] = 2*Join[{0}, a[n - 2], {0}] + 2*Join[{-1/2}, a[n - 1]] + 2*Join[a[n - 1], {-1/2}]'

%t Table[a[n], {n, 0, 10}]

%t Flatten[%]

%K nonn,uned,tabl,obsc

%O 0,5

%A _Roger L. Bagula_, Dec 09 2008