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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Antidiaognal sums are 2, 3, 6, 12, 33, 112, 458, 2151, 11334, 65972,.... LINKS 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

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)