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A144172 Eigentriangle, row sums = A076739, the number of compositions into Fibonacci numbers. 1
1, 1, 1, 1, 1, 2, 0, 1, 2, 4, 1, 0, 2, 4, 7, 0, 1, 0, 4, 7, 14, 0, 0, 2, 0, 7, 14, 26, 1, 0, 0, 4, 0, 14, 26, 49, 0, 1, 0, 0, 7, 0, 26, 49, 94, 0, 0, 2, 0, 0, 14, 0, 49, 94, 177, 0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336, 0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Row sums = A076739 starting with offset 1: (1, 2, 4, 7, 14, 26, 49,...).

Left border = A010056, the characteristic function of the Fibonacci numbers Starting with offset 1: (1, 1, 1, 0, 1,...).

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

Right border = A076739.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

T(n,k) = A010056(n-k+1)*A076739(k-1). A010056, the characteristic function of the Fibonacci numbers, starts with offset 1: (1, 1, 1, 0, 1,...). A076739(k-1), the INVERTi transform of (1, 1, 1, 0, 1,...) starts with offset 0: (1, 1, 2, 4, 7, 14,...).

EXAMPLE

First few rows of the triangle =

1;

1, 1;

1, 1, 2;

0, 1, 2, 4;

1, 0, 2, 4, 7;

0, 1, 0, 4, 7, 14;

0, 0, 2, 0, 7, 14, 26;

1, 0, 0, 4, 0, 14, 26, 49;

0, 1, 0, 0, 7, 0, 26, 49, 94;

0, 0, 2, 0, 0, 14, 0, 49, 94, 177;

0, 0, 0, 4, 0, 0, 26, 0, 94, 177, 336;

0, 0, 0, 0, 7, 0, 0, 49, 0, 177, 336, 637;

1, 0, 0, 0, 0, 14, 0, 0, 94, 0, 336, 637, 1206;

...

Example: row 5 = (1, 0, 2, 4, 7) = termwise product of (1, 0, 1, 1, 1) and (1, 1, 2, 4, 7).

CROSSREFS

A076739, Cf. A010056

Sequence in context: A117316 A109189 A264157 * A227318 A166692 A046766

Adjacent sequences:  A144169 A144170 A144171 * A144173 A144174 A144175

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Sep 12 2008

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)