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Revision History for A118654

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A118654

Square array T(n,k) read by antidiagonals: T(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2).
(history; published version)

#20 by Bruno Berselli at Mon Dec 05 06:12:58 EST 2016

STATUS

reviewed

approved

#19 by Joerg Arndt at Mon Dec 05 06:00:09 EST 2016

STATUS

proposed

reviewed

Discussion

Mon Dec 05

06:10

Jon E. Schoenfield: Okay, thanks again!

#18 by Jon E. Schoenfield at Mon Dec 05 05:57:45 EST 2016

STATUS

editing

proposed

Discussion

Mon Dec 05

06:00

Joerg Arndt: Yes, I think so.

#17 by Jon E. Schoenfield at Mon Dec 05 05:57:20 EST 2016

FORMULA

T(n,k) = A109754(2^n-2, k+1) = A101220(2^n-2, 0, k+1), for n > 0.

CROSSREFS

Cf. T(n,k) = A109754(2^n-2, k+1) = A101220(2^n-2, 0, k+1), for n > 0.

STATUS

proposed

editing

Discussion

Mon Dec 05

05:57

Jon E. Schoenfield: Thanks!  Is this an okay place to put it?

#16 by Jon E. Schoenfield at Mon Dec 05 05:43:51 EST 2016

STATUS

editing

proposed

Discussion

Mon Dec 05

05:55

Joerg Arndt: Yes, formulas should really be in formula section.

#15 by Jon E. Schoenfield at Mon Dec 05 05:35:09 EST 2016

FORMULA

aT(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2).

aT(n,k) = (2^n-2)*Fibonacci(k) + Fibonacci(k+1).

aT(n,0) = 1; aT(n,1) = 2^n - 1; aT(n,k) = aT(n,k-1) + aT(n,k-2), for k > 1.

aT(0,k) = Fibonacci(k-1); aT(1,k) = Fibonacci(k+1); aT(n,k) = 3a3T(n-1,k) - 2a2T(n-2,k), for n > 1.

aT(n,k) = 2a2T(n-1,k) + Fibonacci(k-2), for n > 0.

Sum_{k=0..n} aT(n-k, k) = A119587(n+1). - Ross La Haye, May 31 2006

EXAMPLE

aT(2,3) = 7 because 2^2(Fibonacci(3)) - Fibonacci(3-2) = 4*2 - 1 = 7.

CROSSREFS

Cf. aT(n, k) = A109754(2^n-2, k+1) = A101220(2^n-2, 0, k+1), for n > 0.

Rows: aT(0, k) = A000045(k-1), for k > 0; aT(1, k) = A000045(k+1); aT(2, k) = A000032(k+1); aT(3, k) = A022097(k); aT(4, k) = A022105(k); aT(5, k) = A022401(k).

Columns: aT(n, 1) = A000225(n); aT(n, 2) = A000079(n); aT(n, 3) = A000225(n+1); aT(n, 4) = A055010(n+1); aT(n, 5) = A051633(n); a(n, T,6) = A036563(n+3).

STATUS

proposed

editing

Discussion

Mon Dec 05

05:41

Jon E. Schoenfield: @Michel -- Interesting ... I don't remember having seen that page before ... maybe I did see it, but it was a very long time ago.  Given the "Author(s)" and "Extension" lines in the example at the top of that page (with email addresses and what are now nonstandard date formats), I'm inclined to view that page as being at least rather old, and likely obsolete.  I wonder if it should be edited...?

05:42

Jon E. Schoenfield: @Joerg -- 'works for me -- thanks!

05:43

Jon E. Schoenfield: In the Crossrefs section, the "Rows:" and "Columns:" entries seem to me to fit okay there, but I'm wondering whether the "Cf. T(n,k) = A109754(2^n-2, k+1) = A101220(2^n-2, 0, k+1), for n > 0." entry fits better there or in the Formula section...

#14 by Joerg Arndt at Mon Dec 05 04:26:28 EST 2016

STATUS

editing

proposed

#13 by Joerg Arndt at Mon Dec 05 04:26:11 EST 2016

NAME

Matrix, aSquare array T(n,k) read by antidiagonals: T(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2), read by antidiagonals.

STATUS

proposed

editing

Discussion

Mon Dec 05

04:26

Joerg Arndt: Like this?

#12 by Jon E. Schoenfield at Sun Dec 04 20:56:55 EST 2016

STATUS

editing

proposed

Discussion

Mon Dec 05

00:31

Michel Marcus: a vs T : Not necessarily if we follow 3rd bullet of https://oeis.org/eishelp2.html#NA ??

#11 by Jon E. Schoenfield at Sun Dec 04 20:56:04 EST 2016

NAME

Matrix, a(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2), read by anti-diagonalsantidiagonals.

STATUS

proposed

editing

Discussion

Sun Dec 04

20:56

Jon E. Schoenfield: Should "Matrix" be "Table"?
Should each "a( _ , _ )" be changed to "T( _, _ )"?