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A175353 Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)). 0

%I

%S 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,

%T 1,4374,239,53,19,8,4,2,1,13122,577,117,40,17,8,4,2,1

%N Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).

%C Row sums are {0, 2, 7, 22, 64, 187, 545, 1597, 4700, 13888, ...};

%C I reversed the signs on Riordan's Fibonacci function.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 125 and 155.

%F G.f.: f(x,m) = (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).

%e {2},

%e {6, 1},

%e {18, 3, 1},

%e {54, 7, 2, 1},

%e {162, 17, 5, 2, 1},

%e {486, 41, 11, 4, 2, 1},

%e {1458, 99, 24, 9, 4, 2, 1},

%e {4374, 239, 53, 19, 8, 4, 2, 1},

%e {13122, 577, 117, 40, 17, 8, 4, 2, 1}

%t f[x_, n_] = (x + x^(m + 1))/(1 - 2*x - x^(m + 1));

%t a = Table[Table[SeriesCoefficient[

%t Series[f[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 0, 10}];

%t Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}];

%t Flatten[%]

%Y Cf. A175331.

%K nonn,tabl

%O 0,1

%A _Roger L. Bagula_, Dec 03 2010

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Last modified March 31 16:02 EDT 2020. Contains 333151 sequences. (Running on oeis4.)