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 A106314 Triangle composed of squares, row sums = Paraffin numbers. 5
 1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 9, 4, 1, 1, 4, 9, 9, 4, 1, 1, 4, 9, 16, 9, 4, 1, 1, 4, 9, 16, 16, 9, 4, 1, 1, 4, 9, 16, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 25, 16, 9, 4, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums = A005993, Paraffin numbers: 1, 2, 6, 10, 19, 28, 44, 60... Row sums are; {1, 2, 6, 10, 19, 28, 44, 60, 85, 110, 146,...} LINKS FORMULA Given the triangle of A003983, replace each of the terms by its square. p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= ( then than equal) Floor[n/2], 2*i + 1, -(2*(n - i) + 1)]], {i, 0, n}]/(1 - x); t(n,m)=coefficients(p(x,n),x) EXAMPLE The triangle of A003983 is: 1; 1, 1; 1, 2, 1; 1, 2, 2, 1; 1, 2, 3, 2, 1; ... Replacing each term by its square, we get: 1; 1, 1; 1, 4, 1; 1, 4, 4, 1; 1, 4, 9, 4, 1; ... {1}, {1, 1}, {1, 4, 1}, {1, 4, 4, 1}, {1, 4, 9, 4, 1}, {1, 4, 9, 9, 4, 1}, {1, 4, 9, 16, 9, 4, 1}, {1, 4, 9, 16, 16, 9, 4, 1}, {1, 4, 9, 16, 25, 16, 9, 4, 1}, {1, 4, 9, 16, 25, 25, 16, 9, 4, 1}, {1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1} (End) MATHEMATICA Clear[p, n, i]; p[x_, n_] = Sum[x^i*If[i ==Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], 2*i + 1, -(2*(n - i) + 1)]], {i, 0, n}]/(1 - x); Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}]; Flatten[%] CROSSREFS Cf. A003983, A106314, A005993. Sequence in context: A046596 A174093 A204028 * A152716 A183374 A176263 Adjacent sequences:  A106311 A106312 A106313 * A106315 A106316 A106317 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Apr 28 2005 EXTENSIONS Additional comments from Roger L. Bagula and Gary W. Adamson, Apr 02 2009 STATUS approved

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