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A027170 Triangular array T read by rows (4-diamondization of Pascal's triangle). Step 1: t(n,k) = C(n+2,k+1) + C(n+1,k) + C(n+1,k+1) + C(n,k). Step 2: T(n,k) = t(n,k) - t(0,0) + 1. Domain: 0 <= k <= n, n >= 0. 16
1, 3, 3, 5, 10, 5, 7, 19, 19, 7, 9, 30, 42, 30, 9, 11, 43, 76, 76, 43, 11, 13, 58, 123, 156, 123, 58, 13, 15, 75, 185, 283, 283, 185, 75, 15, 17, 94, 264, 472, 570, 472, 264, 94, 17, 19, 115, 362, 740, 1046, 1046, 740, 362, 115, 19, 21, 138, 481, 1106, 1790, 2096, 1790, 1106, 481, 138, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Rows of n = 0..125 of triangle, flattened

EXAMPLE

Triangle starts:

   1;

   3,  3;

   5, 10,  5;

   7, 19, 19,  7;

   9, 30, 42, 30,  9;

  11, 43, 76, 76, 43, 11;

  ...

MATHEMATICA

t[n_, k_]:= Binomial[n + 2, k + 1] + 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, 10}, {k, 0, n}]] (* Indranil Ghosh, Mar 13 2017 *)

PROG

(PARI) alias(C, binomial);

t(n, k) = C(n+2, k+1)+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+2, k+1) + 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, A026907.

Sequence in context: A146926 A000198 A202674 * A132775 A174102 A217521

Adjacent sequences:  A027167 A027168 A027169 * A027171 A027172 A027173

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)