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A143929 Eigentriangle by rows, termwise products of the natural numbers decrescendo and the bisected Fibonacci series. 1
1, 2, 1, 3, 2, 3, 4, 3, 6, 8, 5, 4, 9, 16, 21, 6, 5, 12, 24, 42, 55, 7, 6, 15, 32, 63, 110, 144, 8, 7, 18, 40, 84, 165, 288, 377, 9, 8, 21, 48, 105, 220, 432, 754, 987, 10, 9, 24, 56, 126, 275, 576, 1131, 1974, 2584 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = even indexed Fibonacci terms A001906.

Sum of n-th row terms = rightmost term of next row.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Given A004736: (1; 2,1; 3,2,1; 4,3,2,1; ...), we apply the termwise products of the sequence A088305(n-1)}_{n>=1} starting (1, 1, 3, 8, 21, ...).

From Wolfdieter Lang, Jan 07 2021: (Start)

T(n, m) = 0 if n < m; T(n, 1) = n, for n >= 1, and T(n, m) = F(2*(m-1))*(n-m+1) for n >= m >= 2, with F = A000045 (Fibonacci).

G.f. column m: G(1, x) = x/(1-x)^2, G(m, x) = F(2*(m-1))*x^m/(1-x)^2, for m >= 2. (End)

With offset 0: g.f. of row polynomials R(n, x) := Sum_{m=0..n} t(n, m)*x^m, that is, g.f. of triangle t(n,m) = T(n+1, m+1):

G(z, x) = (1 - x*z)^2 / ((1 - z)^2*(1 - 3*x*z + (x*z)^2)). - Wolfdieter Lang, Apr 09 2021

EXAMPLE

First rows of the triangle T(n, m), n >= 1, m = 1..n:

  1;

  2, 1;

  3, 2,  3;

  4, 3,  6,  8;

  5, 4,  9, 16,  21;

  6, 5, 12, 24,  42,  55;

  7, 6, 15, 32,  63, 110, 144;

  8, 7, 18, 40,  84, 165, 288, 377;

  9, 8, 21, 48, 105, 220, 432, 754, 987;

  ...

Example: row 4 = (4, 3, 6, 8) = termwise product of (4, 3, 2, 1) and (1, 1, 3, 8).

CROSSREFS

Cf. A000045, A001906, A004736, A088305.

Sequence in context: A115872 A133926 A144337 * A153583 A346797 A029163

Adjacent sequences:  A143926 A143927 A143928 * A143930 A143931 A143932

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Sep 05 2008

STATUS

approved

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)