The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A013610 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A013610

Triangle of coefficients in expansion of (1+3*x)^n.
(history; published version)

#63 by Joerg Arndt at Tue Feb 11 01:23:29 EST 2025

STATUS

editing

proposed

#62 by Joerg Arndt at Tue Feb 11 01:23:09 EST 2025

FORMULA

T(0,0)=1, T(n,k)=3T3*T(n-1,k-1)+T(n-1,k) for 0<=k<=n, T(n,k)=0 for k<0 or k>n _. - _Oliver Seipel_, Feb 10 2025

STATUS

proposed

editing

#61 by Oliver Seipel at Mon Feb 10 14:13:47 EST 2025

STATUS

editing

proposed

Discussion

Mon Feb 10

14:43

Michel Marcus: please fix signature (see signatures above yours)

14:43

Michel Marcus: a program is only useful to people who know that specific language

#60 by Oliver Seipel at Mon Feb 10 14:11:11 EST 2025

FORMULA

T(0,0)=1, T(n,k)=3T(n-1,k-1)+T(n-1,k) for 0<=k<=n, T(n,k)=0 for k<0 or k>n Oliver Seipel, Feb 10 2025

Discussion

Mon Feb 10

14:13

Oliver Seipel: I added a formula, but I think a program is more useful, because it is free of typos,

#59 by Sean A. Irvine at Fri Feb 07 21:18:24 EST 2025

STATUS

proposed

editing

#58 by Oliver Seipel at Sun Jan 26 12:25:03 EST 2025

STATUS

editing

proposed

Discussion

Sun Jan 26

15:01

Michel Marcus: new code is based on a formula ?

18:18

Kevin Ryde: Jean-François' code goes straight to the answer.  Are you superior to that?

Tue Jan 28

06:34

Michel Marcus: you should rather make this a formula than a program ?

Fri Feb 07

21:18

Sean A. Irvine: I agree with Michel, this would be more useful as a formula. Can you do that please?

#57 by Oliver Seipel at Sun Jan 26 12:24:18 EST 2025

MATHEMATICA

T[0, 0] := 1; T[n_, k_]/; 0<=k<=n := T[n, k] = 3T[n-1, k-1]+T[n-1, k]; T[n_, k_] := 0; GridFlatten@Table[T[n, k], {n, 0, 7}, {k, 0, n}] (* Oliver Seipel, Jan 26 2025 *)

#56 by Oliver Seipel at Sun Jan 26 12:22:45 EST 2025

MATHEMATICA

T[0, 0] := 1; T[n_, k_]/; 0<=k<=n := T[n, k] = 3T[n-1, k-1]+T[n-1, k]; T[n_, k_] := 0; Grid@Table[T[n, k], {n, 0, 7}, {k, 0, n}] (* Oliver Seipel, Jan 26 2025 *)

STATUS

approved

editing

#55 by Charles R Greathouse IV at Thu Sep 08 08:44:38 EDT 2022

PROG

(MAGMAMagma) [3^k*Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 19 2021

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#54 by Michel Marcus at Fri May 21 01:14:00 EDT 2021

STATUS

reviewed

approved