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 A175353 Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)). 0
 2, 6, 1, 18, 3, 1, 54, 7, 2, 1, 162, 17, 5, 2, 1, 486, 41, 11, 4, 2, 1, 1458, 99, 24, 9, 4, 2, 1, 4374, 239, 53, 19, 8, 4, 2, 1, 13122, 577, 117, 40, 17, 8, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are {0, 2, 7, 22, 64, 187, 545, 1597, 4700, 13888, ...}; I reversed the signs on Riordan's Fibonacci function. REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 125 and 155. LINKS FORMULA G.f.: f(x,m) = (x + x^(m + 1))/(1 - 2*x - x^(m + 1)). EXAMPLE {2}, {6, 1}, {18, 3, 1}, {54, 7, 2, 1}, {162, 17, 5, 2, 1}, {486, 41, 11, 4, 2, 1}, {1458, 99, 24, 9, 4, 2, 1}, {4374, 239, 53, 19, 8, 4, 2, 1}, {13122, 577, 117, 40, 17, 8, 4, 2, 1} MATHEMATICA f[x_, n_] = (x + x^(m + 1))/(1 - 2*x - x^(m + 1)); a = Table[Table[SeriesCoefficient[       Series[f[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 0, 10}]; Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}]; Flatten[%] CROSSREFS Cf. A175331. Sequence in context: A280836 A281307 A281417 * A181307 A008855 A181299 Adjacent sequences:  A175350 A175351 A175352 * A175354 A175355 A175356 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 03 2010 STATUS approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)