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A236830 Riordan array (1/(1-x*C(x)^3), x*C(x)), C(x) the g.f. of A000108. 12
1, 1, 1, 4, 2, 1, 16, 7, 3, 1, 65, 27, 11, 4, 1, 267, 108, 43, 16, 5, 1, 1105, 440, 173, 65, 22, 6, 1, 4597, 1812, 707, 267, 94, 29, 7, 1, 19196, 7514, 2917, 1105, 398, 131, 37, 8, 1, 80380, 31307, 12111, 4597, 1680, 575, 177, 46, 9, 1, 337284, 130883, 50503 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

T(n+3,n) = A011826(n+5).

LINKS

Table of n, a(n) for n=0..57.

FORMULA

Sum_{k=0..n} T(n,k) = A026726(n).

G.f.: 1/((x^2*C(x)^4-x*C(x))*y-x*C(x)^3+1), where C(x) the g.f. of A000108. - Vladimir Kruchinin, Apr 22 2015

From Peter Bala, Feb 18 2018: (Start)

T(n,k) = Sum_{i = 0..n-k} Fibonacci(2*i-1)*binomial(2*n-2-k-i,n-k-i).

The n-th row polynomial of row reverse triangle is the n-th degree Taylor polynomial of the rational function (1 - 3*x + 2*x^2)/(1 - 3*x + x^2) * 1/(1 - x)^n about 0. For example, for n = 4, (1 - 3*x + 2*x^2)/(1 - 3*x + x^2) * 1/(1 - x)^4 = 1 + 4*x + 11*x^2 + 27*x^3 + 65*x^4 + O(x^5), giving row 4 as (65, 27, 11, 4, 1). (End)

EXAMPLE

Triangle begins:

      1;

      1,    1;

      4,    2,    1;

     16,    7,    3,    1;

     65,   27,   11,    4,   1;

    267,  108,   43,   16,   5,   1;

   1105,  440,  173,   65,  22,   6,  1;

   4597, 1812,  707,  267,  94,  29,  7, 1;

  19196, 7514, 2917, 1105, 398, 131, 37, 8, 1;

Production matrix is:

   1  1

   3  1   1

   6  1   1   1

  10  1   1   1   1

  15  1   1   1   1   1

  21  1   1   1   1   1   1

  28  1   1   1   1   1   1   1

  36  1   1   1   1   1   1   1   1

  45  1   1   1   1   1   1   1   1   1

  55  1   1   1   1   1   1   1   1   1   1

  66  1   1   1   1   1   1   1   1   1   1   1

  78  1   1   1   1   1   1   1   1   1   1   1   1

  91  1   1   1   1   1   1   1   1   1   1   1   1   1

  ...

MAPLE

A236830 := (n, k) -> add(combinat:-fibonacci(2*i-1)*binomial(2*n-2-k-i, n-k-i), i = 0..n-k): seq(seq(A236830(n, k), k = 0..n), n = 0..10); # Peter Bala, Feb 18 2018

CROSSREFS

Cf. (columns): A165201, A026726, A026671, A026674, A026672, A026675, A026673, A026843, A026842 or A026846 or A026849, A026844, A026841 or A026848.

Sequence in context: A171650 A225476 A143777 * A269736 A264535 A256039

Adjacent sequences:  A236827 A236828 A236829 * A236831 A236832 A236833

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Feb 01 2014

STATUS

approved

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Last modified April 26 04:04 EDT 2019. Contains 322469 sequences. (Running on oeis4.)