The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A026907 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A026907

Triangular array T read by rows (9-diamondization of Pascal's triangle). Step 1: t(n,k) = sum of 9 entries in diamond-shaped subarray of Pascal's triangle having vertices C(n,k), C(n+4,k+2), C(n+2,k), C(n+2,k+2). Step 2: T(n,k) = t(n,k) - t(0,0) + 1.
(history; published version)

#22 by Michel Marcus at Sat Apr 18 09:21:36 EDT 2020

STATUS

reviewed

approved

#21 by Joerg Arndt at Sat Apr 18 09:19:20 EDT 2020

STATUS

proposed

reviewed

#20 by Joerg Arndt at Sat Apr 18 09:19:16 EDT 2020

STATUS

editing

proposed

#19 by Joerg Arndt at Sat Apr 18 09:19:12 EDT 2020

PROG

tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print()); \\ _Michel Marcus_, Mar 13 2017

(Python)

import math

f=math.factorial

def C(n, r): return f(n)/f(r)/f(n - r)

def t(n, k): return C(n + 4, k + 2) + C(n + 3, k + 1) + C(n + 3, k + 2) + C(n + 2, k) + C(n + 2, k + 1) + C(n + 2, k + 2) + C(n + 1, k) + C(n + 1, k + 1) + C(n, k)

i=0

for n in range(126):

for k in range(n+1):

print(str(i)+" "+str(t(n, k) - t(0, 0) + 1))

i+=1 # _Indranil Ghosh_, \\ _Michel Marcus_, Mar 13 2017

STATUS

proposed

editing

#18 by F. Chapoton at Sat Apr 18 04:18:31 EDT 2020

STATUS

editing

proposed

Discussion

Sat Apr 18

04:28

Michel Marcus: exemple of output : 2 13.0

#17 by F. Chapoton at Sat Apr 18 04:18:18 EDT 2020

PROG

for n in range(0, 126):

.... for k in range(0, n+1):

........ print (str(i)+" "+str(t(n, k) - t(0, 0) + 1))

........ i+=1 # Indranil Ghosh, Mar 13 2017

STATUS

approved

editing

Discussion

Sat Apr 18

04:18

F. Chapoton: python code: use space to indent and adapt to py3

#16 by N. J. A. Sloane at Tue Mar 14 00:10:12 EDT 2017

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Mon Mar 13 22:53:47 EDT 2017

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Mon Mar 13 22:53:43 EDT 2017

NAME

Triangular array T read by rows (9-diamondization of Pascal's triangle). Step 1: t(n,k) = sum of 9 entries in diamond-shaped subarray of Pascal's triangle having vertices C(n,k), C(n+4,k+2), C(n+2,k), C(n+2,k+2). Step 2: T(n,k) = t(n,k) - t(0,0) + 1.

EXAMPLE

1,;

13, 13,;

28, 44, 28,;

46, 90, 90, 46,;

67, 154, 198, 154, 67,;

91, 239, 370, 370, 239, 91,;

...

STATUS

proposed

editing

#13 by Indranil Ghosh at Mon Mar 13 16:56:28 EDT 2017

STATUS

editing

proposed