|
%I #6 May 15 2016 23:37:19
%S 2,1,2,3,1,2,4,5,1,2,7,16,7,1,2,11,53,36,9,1,2,18,175,187,64,11,1,2,
%T 29,578,971,457,100,13,1,2,47,1909,5042,3263,911,144,15,1,2,76,6305,
%U 26181,23298,8299,1597,196,17,1,2
%N Array read by antidiagonals: T(0,m)=2, T(1,m)=1, T(n,m)=A000032(n) and recursively T(n,m)=( T(n-1,m)^2 + (4*m + 1)*(-1)^n) / T(n-2, m), n>=0, m>=1.
%C Antidiaognal sums are 2, 3, 6, 12, 33, 112, 458, 2151, 11334, 65972,....
%e 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ,...
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
%e 3, 5, 7, 9, 11, 13, 15, 17, 19, 21,...
%e 4, 16, 36, 64, 100, 144, 196, 256, 324, 400,...
%e 7, 53, 187, 457, 911,1597,2563,3857,5527,7621,...
%p A178030 := proc(n,k)
%p if k = 0 then
%p A000032(n);
%p elif n = 0 then
%p 2 ;
%p elif n = 1 then
%p 1 ;
%p else
%p (procname(n-1,k)^2+(4*k+1)*(-1)^n)/procname(n-2,k) ;
%p end if;
%p end proc: # _R. J. Mathar_, May 15 2016
%t f[0, a_] := 2; f[1, a_] := 1;
%t f[n_, a_] := f[n, a] = (f[n - 1, a]^2 - (4*a + 1)*(-1)^(n - 1))/f[n - 2, a];
%t a = Table[Table[f[n, m], {n, 0, 10}], {m, 1, 11}];
%t Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
%t Flatten[%]
%Y Cf. A000032.
%K nonn,tabl,easy
%O 0,1
%A _Roger L. Bagula_, May 17 2010
|
