The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A152920

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A152920

Triangle read by rows: triangle A062111 reversed.
(history; published version)

#35 by N. J. A. Sloane at Wed Sep 28 18:52:54 EDT 2022

STATUS

proposed

approved

#34 by Michel Marcus at Wed Sep 28 02:04:35 EDT 2022

STATUS

editing

proposed

Discussion

Wed Sep 28

18:25

N. J. A. Sloane: >  remove A001787, from 2nd xrefs line ?  No!  Why remove it?  It is mentioned in the formulas.

18:43

G. C. Greubel: A001787 was duplicated in Cf section -> duplicate was removed.

#33 by Michel Marcus at Wed Sep 28 02:04:26 EDT 2022

CROSSREFS

Columns and diagonals: A001787, A001792, A034007, A045623, A045891, A111297, A159694, A159695, A159696, A159697. [_Philippe Deléham_, Apr 20 2009]

STATUS

proposed

editing

Discussion

Wed Sep 28

02:04

Michel Marcus: ok ?

#32 by G. C. Greubel at Wed Sep 28 01:59:40 EDT 2022

STATUS

editing

proposed

#31 by G. C. Greubel at Wed Sep 28 01:59:33 EDT 2022

CROSSREFS

Cf. A001787, A053220, A058877 (row sums), A193844, A212697.

Columns and diagonals: A001787, A001792, A034007, A045623, A045891, A034007, A111297, A159694, A159695, A159696, A159697. [Philippe Deléham, Apr 20 2009]

STATUS

proposed

editing

#30 by G. C. Greubel at Tue Sep 27 18:17:19 EDT 2022

STATUS

editing

proposed

Discussion

Wed Sep 28

01:57

Michel Marcus: remove A001787, from 2nd xrefs line ?

#29 by G. C. Greubel at Tue Sep 27 18:17:07 EDT 2022

FORMULA

T(n, n-1) = A001792(n).

T(m*n, n) = (2*m-1) = A001792*A001787(n), for m >= 1. (End)

T(n, n) = A001787(n). (End)

#28 by G. C. Greubel at Tue Sep 27 18:03:20 EDT 2022

FORMULA

Row sums: (2^n-1)(n+1) = A058877(n). [_- _R. J. Mathar_, Jan 22 2009]

T(2n, n) = 3*n*2^(n-1) = 3*A001787(n). [_- _Philippe Deléham_, Apr 20 2009]

T(n, k) = (2*n-k) * 2^(k-1) for 0 <= k <= n.

T(n, k) = T(n, k-1) + T(n-1, k-1) for k>=1, T(n,0) = n. - Alois P. Heinz, Sep 12 2022

From G. C. Greubel, Sep 27 2022: (Start)

T(2*n-1, n-1) = A053220(n).

T(2*n+1, n-1) = 3*A001792(n).

T(n, n-1) = A001792(n).

T(n, n) = A001787(n). (End)

EXAMPLE

1, 1;

2, 3, 4;

3, 5, 8, 12;

4, 7, 12, 20, 32;

MATHEMATICA

t[0, k_] := k; t[n_, k_] := t[n, k] = t[n - 1, k] + t[n - 1, k + 1]; Table[t[n - k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Sep 11 2016 *)

Table[t[n-k, k], {n, 0, 10}, {k, n, 0, -1}]//Flatten (* Jean-François Alcover, Sep 11 2016 *)

PROG

(Magma) [2^k*(n-k/2): k in [0..n], n in [0..12]]; // G. C. Greubel, Sep 27 2022

(SageMath) flatten([[2^(k-1)*(2*n-k) for k in range(n+1)] for n in range(12)]) # G. C. Greubel, Sep 27 2022

CROSSREFS

Cf. A001787, A053220, A058877 (row sums), A193844, A212697.

STATUS

approved

editing

#27 by Alois P. Heinz at Mon Sep 12 08:34:48 EDT 2022

STATUS

editing

approved

#26 by Alois P. Heinz at Mon Sep 12 08:34:44 EDT 2022

FORMULA

Row sums: (2^n-1)(n+1) = A058877(n). [R. J. Mathar, Jan 22 2009]

STATUS

approved

editing