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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.
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,....
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
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, May 17 2010
STATUS
approved