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A171142 Triangle T(n,k) of the coefficients [x^k] of the polynomial p_n(x), where p_n(x)=(1+x)*p_{n-1}(x) if n even, p_n(x) = (x^2+4x+1)^((n-1)/2) if n odd. 4
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 8, 18, 8, 1, 1, 9, 26, 26, 9, 1, 1, 12, 51, 88, 51, 12, 1, 1, 13, 63, 139, 139, 63, 13, 1, 1, 16, 100, 304, 454, 304, 100, 16, 1, 1, 17, 116, 404, 758, 758, 404, 116, 17, 1, 1, 20, 165, 720, 1770, 2424, 1770, 720, 165, 20, 1, 1, 21, 185, 885 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are apparently in A026549.

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

The triangle starts in row n=1 with column 0<=k<n as:

1;

1, 1;

1, 4, 1;

1, 5, 5, 1;

1, 8, 18, 8, 1;

1, 9, 26, 26, 9, 1;

1, 12, 51, 88, 51, 12, 1;

1, 13, 63, 139, 139, 63, 13, 1;

1, 16, 100, 304, 454, 304, 100, 16, 1;

1, 17, 116, 404, 758, 758, 404, 116, 17, 1;

1, 20, 165, 720, 1770, 2424, 1770, 720, 165, 20, 1;

1, 21, 185, 885, 2490, 4194, 4194, 2490, 885, 185, 21, 1;

MAPLE

A171142P := proc(n) option remember; if type(n, 'even') then (x+1)*procname(n-1) ; else (x^2+4*x+1)^((n-1)/2) ; end if; expand(%) ; end proc:

A171142 := proc(n, k) coeff(A171142P(n, x), x, k) ; end proc:

MATHEMATICA

Clear[p, n, x, a]

w = 4;

p[x, 1] := 1;

p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, (x + 1)*p[x, n - 1], (x^2 + w*x + 1)^Floor[n/2]];

a = Table[CoefficientList[p[x, n], x], {n, 1, 12}];

Flatten[a]

CROSSREFS

Cf. A051159, A169623, A007318

Sequence in context: A156050 A136489 A166455 * A174037 A173077 A131239

Adjacent sequences:  A171139 A171140 A171141 * A171143 A171144 A171145

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Dec 04 2009

STATUS

approved

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Last modified July 19 04:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)