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A140819 Coefficients of Hodge diamond GCD 'X' matrices as polynomials: matrix example; M={{2,0,2}. {0,1,0], {2,0,2}: M(d, x, y)= Sum[Sum[If[n == m, GCD[d - 1, m - 1], If[n == d - m + 1, GCD[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] . 0
2, 2, 4, 1, 4, 6, 2, 2, 6, 8, 2, 2, 2, 8, 10, 2, 2, 2, 2, 10, 12, 2, 4, 3, 4, 2, 12, 14, 2, 2, 2, 2, 2, 2, 14, 16, 2, 4, 2, 4, 2, 4, 2, 16, 18, 2, 2, 6, 2, 2, 6, 2, 2, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{0, 4, 9, 16, 22, 28, 39, 40, 52, 60}.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

M(d, x, y)= Sum[Sum[If[n == m, GCD[d - 1, m - 1], If[n == d - m + 1, GCD[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] ; a(n,m)=Coefficients(M(n,x,1)).

EXAMPLE

{0},

{2, 2},

{4, 1, 4},

{6, 2, 2, 6},

{8, 2, 2, 2, 8},

{10, 2, 2, 2, 2, 10},

{12, 2, 4, 3, 4, 2, 12},

{14, 2, 2, 2, 2, 2, 2, 14},

{16, 2, 4, 2, 4, 2, 4, 2, 16},

{18, 2, 2, 6, 2, 2, 6, 2, 2, 18}

MATHEMATICA

Clear[M, y, x] M[d_, x_, y_] := Sum[Sum[If[n == m, GCD[d - 1, m - 1], If[n == d - m + 1, GCD[ d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] Table[CoefficientList[M[d, x, 1], x], {d, 1, 10}] Flatten[%] Table[Apply[Plus, CoefficientList[M[d, x, 1], x]], {d, 1, 10}]

CROSSREFS

Cf. A140685.

Sequence in context: A023137 A327488 A065273 * A138558 A111580 A066202

Adjacent sequences:  A140816 A140817 A140818 * A140820 A140821 A140822

KEYWORD

nonn

AUTHOR

Roger L. Bagula and Mats Granvik, Jul 16 2008

STATUS

approved

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Last modified April 14 15:18 EDT 2021. Contains 342949 sequences. (Running on oeis4.)