The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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