A152251 Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.

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

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