A174301 A symmetrical triangle: T(n,k) = binomial(n, k)*if(floor(n/2) greater than or equal to k then 4^k, otherwise 4^(n-k)).

1, 1, 1, 1, 8, 1, 1, 12, 12, 1, 1, 16, 96, 16, 1, 1, 20, 160, 160, 20, 1, 1, 24, 240, 1280, 240, 24, 1, 1, 28, 336, 2240, 2240, 336, 28, 1, 1, 32, 448, 3584, 17920, 3584, 448, 32, 1, 1, 36, 576, 5376, 32256, 32256, 5376, 576, 36, 1, 1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40, 1

Offset: 0

Author

Roger L. Bagula, Mar 15 2010

Keywords

• nonn
• tabl

Comments

Row sums are: {1, 2, 10, 26, 130, 362, 1810, 5210, 26050, 76490, ...}.

Examples

			Triangle begins:
  1;
  1,  1;
  1,  8,   1;
  1, 12,  12,    1;
  1, 16,  96,   16,     1;
  1, 20, 160,  160,    20,      1;
  1, 24, 240, 1280,   240,     24,     1;
  1, 28, 336, 2240,  2240,    336,    28,    1;
  1, 32, 448, 3584, 17920,   3584,   448,   32,   1;
  1, 36, 576, 5376, 32256,  32256,  5376,  576,  36,  1;
  1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40,  1;
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A144463, A144470.

T(2n,n) gives A098430.

Programs

Magma

[[Floor(n/2) ge k select 4^k*Binomial(n,k) else 4^(n-k)*Binomial(n,k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 15 2019

Mathematica

Table[Binomial[n, m]*If[Floor[n/2]>=m , 4^m, 4^(n-m)], {n,0,10}, {m,0,n} ]//Flatten

PARI

{T(n,k) = binomial(n,k)*if(floor(n/2)>=k, 4^k, 4^(n-k))}; \\ G. C. Greubel, Apr 15 2019

Sage

def T(n,k):
   if floor(n/2)>=k: return 4^k*binomial(n,k)
   else: return 4^(n-k)*binomial(n,k)
[[T(n,k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 15 2019

Formula

T(n, m) = binomial(n, m)*if(floor(n/2) greater than or equal to m then 4^m, otherwise 4^(n-m)).

Extensions

Edited by G. C. Greubel, Apr 15 2019