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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. 14
1, 13, 13, 28, 44, 28, 46, 90, 90, 46, 67, 154, 198, 154, 67, 91, 239, 370, 370, 239, 91, 118, 348, 627, 758, 627, 348, 118, 148, 484, 993, 1403, 1403, 993, 484, 148, 181, 650, 1495, 2414, 2824, 2414, 1495, 650, 181, 217, 849, 2163, 3927, 5256, 5256, 3927, 2163, 849, 217 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Rows 0..125, flattened

EXAMPLE

Triangle starts:

   1;

  13,  13;

  28,  44,  28;

  46,  90,  90,  46;

  67, 154, 198, 154,  67;

  91, 239, 370, 370, 239,  91;

  ...

MATHEMATICA

t[n_, k_]:=Binomial[n + 4, k + 2 ] + Binomial[n + 3, k + 1] + Binomial[n + 3, k + 2] + Binomial[n + 2, k] + Binomial[n + 2, k + 1] + Binomial[n + 2, k + 2] + Binomial[n + 1, k] + Binomial[n + 1, k + 1] + Binomial[n, k] ; T[n_, k_]:=t[n, k] - t[0, 0] + 1; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]] (* Indranil Ghosh, Mar 13 2017 *)

PROG

(PARI) alias(C, binomial);

t(n, k) = 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);

T(n, k) = t(n, k)-t(0, 0)+1;

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(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

CROSSREFS

Cf. A007318, A027170.

Sequence in context: A003889 A166545 A022347 * A210475 A214466 A147249

Adjacent sequences:  A026904 A026905 A026906 * A026908 A026909 A026910

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 18 10:28 EDT 2017. Contains 293507 sequences.