A178030 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.

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, 29, 578, 971, 457, 100, 13, 1, 2, 47, 1909, 5042, 3263, 911, 144, 15, 1, 2, 76, 6305, 26181, 23298, 8299, 1597, 196, 17, 1, 2

Offset

0,1

Comments

Antidiaognal sums are 2, 3, 6, 12, 33, 112, 458, 2151, 11334, 65972,....

Links

Table of n, a(n) for n=0..54.

Example

  2,   2,   2,   2,   2,   2,   2,   2,   2,   2, ,...
1,   1,   1,   1,   1,   1,   1,   1,   1,   1,...
3,   5,   7,   9,  11,  13,  15,  17,  19,  21,...
4,  16,  36,  64, 100, 144, 196, 256, 324, 400,...
7,  53, 187, 457, 911,1597,2563,3857,5527,7621,...

Maple

A178030 := proc(n, k)
    if k = 0 then
        A000032(n);
    elif n = 0 then
        2 ;
    elif n = 1 then
        1 ;
    else
        (procname(n-1, k)^2+(4*k+1)*(-1)^n)/procname(n-2, k) ;
    end if;
end proc: # R. J. Mathar, May 15 2016

Mathematica

f[0, a_] := 2; f[1, a_] := 1;
f[n_, a_] := f[n, a] = (f[n - 1, a]^2 - (4*a + 1)*(-1)^(n - 1))/f[n - 2, a];
a = Table[Table[f[n, m], {n, 0, 10}], {m, 1, 11}];
Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]

Crossrefs

Cf. A000032.

Sequence in context: A268956 A208515 A286880 * A131879 A172288 A134628

Adjacent sequences: A178027 A178028 A178029 * A178031 A178032 A178033

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, May 17 2010

Status

approved