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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

Table of n, a(n) for n=0..44.

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.)