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A152251 Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers. 2
1, 1, 1, 2, 1, 2, 4, 2, 2, 5, 8, 4, 4, 5, 13, 16, 8, 8, 10, 13, 34, 32, 16, 16, 20, 26, 34, 89, 64, 32, 32, 40, 52, 68, 89, 233, 128, 64, 64, 80, 104, 136, 178, 233, 610 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums = A001519, the odd-indexed Fibonacci numbers starting (1, 2, 5, 13, 34, ...).

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

LINKS

Table of n, a(n) for n=1..45.

FORMULA

Triangle read by rows, M*Q. M = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in every column and Q = a matrix (1, 1, 2, 5, 13, 34, ...) as the main diagonal and the rest zeros.

Let M = production matrix for reversed rows of the triangle as follows:

  1, 1;

  1, 0, 2;

  1, 0, 0, 2;

  1, 0, 0, 0, 2;

  1, 0, 0, 0, 0, 2;

  ...

Reversal of n-th row of triangle A152251 = top row terms of M^(n-1). Example: top row of M^3 = (5, 2, 2, 4). - Gary W. Adamson, Jul 07 2011

EXAMPLE

First few rows of the triangle =

    1;

    1,   1;

    2,   1,   2;

    4,   2,   2,   5;

    8,   4,   4,   5,  13;

   16,   8,   8,  10,  13,  34;

   32,  16,  16,  20,  26,  34,  89;

   64,  32,  32,  40,  52,  68,  89, 233;

  128,  64,  64,  80, 104, 136, 178, 233, 610;

  ...

Row 4 = (8, 4, 4, 5, 13) = termwise products of (8, 4, 2, 1, 1) and (1, 1, 2, 5, 13).

CROSSREFS

Cf. A001519.

Sequence in context: A082793 A114929 A247321 * A144025 A058573 A184990

Adjacent sequences:  A152248 A152249 A152250 * A152252 A152253 A152254

KEYWORD

eigen,nonn,tabl

AUTHOR

Gary W. Adamson, Nov 30 2008

EXTENSIONS

Last term corrected by Olivier Gérard, Aug 11 2016

STATUS

approved

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Last modified June 16 19:05 EDT 2021. Contains 345068 sequences. (Running on oeis4.)