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A144961 Eigentriangle whose left border is the Padovan sequence, and whose right border and row sums are a modified Fibonacci sequence. 1
1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 1, 1, 0, 1, 0, 0, 5, 1, 1, 1, 0, 2, 0, 0, 8, 2, 1, 1, 1, 0, 3, 0, 0, 13, 2, 2, 1, 1, 2, 0, 5, 0, 0, 21, 3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34, 4, 3, 2, 2, 2, 3, 5, 0, 13, 0, 0, 55, 5, 4, 3, 2, 4, 3, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,15

COMMENTS

Left border = A000931, the Padovan sequence: (1, 0, 0, 1, 0, 1, 1, 1, 2, 2,...).

Right border = (1, 1, 1, 1, 2, 3, 5, 8, 13, 21,...)

Row sums = (1, 1, 1, 2, 3, 5, 8, 13, 21, 34,...).

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

LINKS

Nathaniel Johnston, Rows n = 0..150, flattened

FORMULA

Triangle read by rows, termwise products of a Padovan "decrescendo" triangle: (1; 0,1; 0,0,1; 1,0,0,1,...) and the Fibonacci series preceded by two 1's: (1, 1, 1, 1, 2, 3, 5, 8,...); (i.e. the INVERT transform of the Padovan sequence).

a(n,k) = fibonacci(max(k-1,1))*A000931(n-k). - Nathaniel Johnston, May 05 2011

EXAMPLE

First few rows of the triangle =

1

0 1

0 0 1

1 0 0 1

0 1 0 0 2

1 0 1 0 0 3

1 1 0 1 0 0 5

1 1 1 0 2 0 0 8

2 1 1 1 0 3 0 0 13

2 2 1 1 2 0 5 0  0 21

3 2 2 1 2 3 0 8  0  0 34

4 3 2 2 2 3 5 0 13  0  0 55

...

MAPLE

with(combinat): A000931 := proc(n) option remember: if(n=0)then return 1: elif(n<=2)then return 0: else return procname(n-2)+procname(n-3): fi: end: A144961 := proc(n, k) return fibonacci(max(k-1, 1))*A000931(n-k) end:for n from 0 to 12 do for k from 0 to n do printf("%d, ", A144961(n, k)); od: printf("\n"); od: # Nathaniel Johnston, May 05 2011

CROSSREFS

Cf. A000045, A000931.

Sequence in context: A283000 A145765 A157424 * A144627 A135929 A080733

Adjacent sequences:  A144958 A144959 A144960 * A144962 A144963 A144964

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Sep 27 2008

EXTENSIONS

Example triangle corrected by Nathaniel Johnston, May 05 2011

STATUS

approved

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Last modified October 23 18:50 EDT 2018. Contains 316530 sequences. (Running on oeis4.)