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A226377 Lucas numbers differences triangle T(n,k), k<=n, where column k+1 holds the k-th differences of A000204, read by rows. 1
1, 3, 2, 4, 1, -1, 7, 3, 2, 3, 11, 4, 1, -1, -4, 18, 7, 3, 2, 3, 7, 29, 11, 4, 1, -1, -4, -11, 47, 18, 7, 3, 2, 3, 7, 18, 76, 29, 11, 4, 1, -1, -4, -11, -29, 123, 47, 18, 7, 3, 2, 3, 7, 18, 47, 199, 76, 29, 11, 4, 1, -1, -4, -1, -29, -76, -199 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Consecutive columns (i.e. k =1,2,3...) shift the Lucas sequence (A000204) down by 2 indices.

Diagonal (n=k) produces A061084, and Lucas numbers at increasingly negative indices for n=k>2.

Row sums equal A203976(n) for n=>1, which equals Lucas numbers  A000204(n) if n is odd, and 5 * A000045(2*n) (Fibonacci) if n is even.

Compare A227431 which is a differences triangle for the Fibonacci sequence A000045.

LINKS

Table of n, a(n) for n=1..67.

FORMULA

T(n,1) = A000204(n) for n>0, T(n,k) = T(n,k-1) - T(n-1,k-1).

EXAMPLE

Triangle begins:

1;

3,  2;

4,  1, -1;

7,  3,  2,  3;

11,  4,  1, -1, -4;

18,  7,  3,  2,  3,  7;

29, 11,  4,  1, -1, -4, -11;

47, 18,  7,  3,  2,  3,   7,  18;

76, 29, 11,  4,  1, -1,  -4, -11, -29;

...

CROSSREFS

Cf. A000204, A203976

Sequence in context: A284552 A154879 A097673 * A140430 A123359 A121885

Adjacent sequences:  A226374 A226375 A226376 * A226378 A226379 A226380

KEYWORD

sign,tabl

AUTHOR

Richard R. Forberg, Jul 31 2013

STATUS

approved

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Last modified April 22 14:18 EDT 2019. Contains 322349 sequences. (Running on oeis4.)