A124264 Hilbert-Warren Add Sequence.
2, 5, 20, 51, 312, 740, 15000, 34125, 160720, 4988592, 180774720, 844074000, 27991656000, 66264953040
Offset: 1
Crossrefs
Cf. A124261.
Programs
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Maxima
/* [wxMaxima: input start ] */ load("eigen"); order : 4; X : columnvector(makelist(concat(x,i), i, 1, order)); h[i,j] := (i + j)/(i + j - 1); Unity[i,j] := 1; A : genmatrix(h, order, order); A . X; B : genmatrix(Unity, 1, order); A . X = B; Ap : triangularize(A); Ap . X = B; App : invert(Ap); App . B; /* [wxMaxima: input end ] */
Formula
Terms generated by solving n x n linear system [H']x = b where b is unity and elements of H' are given by H'[i,j] = (i + j)/(i + j - 1). Sequence term is the denominator of last unknown xn. Numerator is unity for last term for all problem orders examined.
Extensions
The author said that this version of the submission was unsatisfactory and set me a better version in email, which may replace this. - N. J. A. Sloane, Oct 24 2006
Comments