A178030 - OEIS

%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