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A104793
Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.
1
1, 5, 1, 13, 5, 1, 28, 13, 5, 1, 54, 28, 13, 5, 1, 98, 54, 28, 13, 5, 1, 171, 98, 54, 28, 13, 5, 1, 291, 171, 98, 54, 28, 13, 5, 1, 487, 291, 171, 98, 54, 28, 13, 5, 1, 806, 487, 291, 171, 98, 54, 28, 13, 5, 1, 1324, 806, 487, 291, 171, 98, 54, 28, 13, 5, 1
OFFSET
1,2
COMMENTS
Repeatedly writing the sequence A023537 backwards.
FORMULA
From Ralf Stephan, Apr 05 2009: (Start)
T(n,k) = Lucas(n-k+4) - (3*n - 3*k + 7).
T(n,k) = A023537(A004736(n, k+1)). (End)
EXAMPLE
First few rows of the triangle are:
1;
5, 1;
13, 5, 1;
28, 13, 5, 1;
54, 28, 13, 5, 1;
98, 54, 28, 13, 5, 1; ...
MATHEMATICA
Table[LucasL[n-k+4] -3*n+3*k-7, {n, 1, 12}, {k, 0, n-1}]//Flatten (* G. C. Greubel, Jun 01 2019 *)
PROG
(PARI) {T(n, k) = fibonacci(n-k+5) + fibonacci(n-k+3) -3*n +3*k - 7}; \\ G. C. Greubel, Jun 01 2019
(Magma) [[Lucas(n-k+4) -(3*n-3*k+7): k in [0..n-1]]: n in [1..12]]; // G. C. Greubel, Jun 01 2019
(Sage) [[lucas_number2(n-k+4, 1, -1) -3*n+3*k-7 for k in (0..n-1)] for n in (1..12)] # G. C. Greubel, Jun 01 2019
(GAP) Flat(List([1..12], n-> List([0..n-1], k-> Lucas(1, -1, n-k+4)[2] -3*n+3*k-7 ))) # G. C. Greubel, Jun 01 2019
CROSSREFS
Row sums are in A027963.
Cf. A104765.
Sequence in context: A327766 A147348 A081224 * A243883 A147004 A319664
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 26 2005
EXTENSIONS
Edited by Ralf Stephan, Apr 05 2009
STATUS
approved