A124265 Variant sequence generated by solving the order n x n linear problem [H]x = b where b is the unit vector and the sequence term is given by the denominator of the last unknown xn.

3, 3, 11, 27, 162, 380, 7650, 17325, 81340, 2518992, 91128240, 424947600, 14078156400, 33300661680, 424624548348

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Formula

[H] is defined by hilbertWarrenA1[i,j]:=(1+j+i)/(-1+j+i) where numbering starts at 1.

Prog

(Maxima) HilbertWarren(fun, order) := ( Unity[i, j] := 1, A : genmatrix(fun, order, order), B : genmatrix(Unity, 1, order), App : invert(triangularize(A)), Xp : App . B, 1/Xp[order] ); findWarrenSequenceTerms(fun, a, b) := ( L : append(), for order: a next order+1 through b do L: cons(first(HilbertWarren(fun, order)), L), S : reverse(L) ); k : 15; hilbert[i, j] := 1/(i + j - 1); findWarrenSequenceTerms(hilbert, 1, k); hilbertA0[i, j] := (i + j + 0)/(i + j - 1); /* sum 1 */ findWarrenSequenceTerms(hilbertA0, 1, k); hilbertA1[i, j] := (i + j + 1)/(i + j - 1); /* sum 2: there are lots of these, increment numerator */ findWarrenSequenceTerms(hilbertA1, 1, k); hilbertD1[i, j] := (i - j + 1)/(i + j - 1); /* difference 1 */ findWarrenSequenceTerms(hilbertD1, 1, k); hilbertP1[i, j] := (i * j + 0)/(i + j - 1); /* product 1 */ findWarrenSequenceTerms(hilbertP1, 1, k); hilbertQ1[i, j] := (i / j)/(i + j - 1); /* quotient 1 */ findWarrenSequenceTerms(hilbertQ1, 1, k);

Crossrefs

Sequence in context: A281101 A341601 A322701 * A163938 A373393 A109937

Adjacent sequences: A124262 A124263 A124264 * A124266 A124267 A124268

Keyword

eigen,frac,hard,nonn

Author

L. Van Warren (van(AT)wdv.com), Oct 23 2006

Status

approved