A227074 A triangle formed like Pascal's triangle, but with 4^n on the borders instead of 1.

1, 4, 4, 16, 8, 16, 64, 24, 24, 64, 256, 88, 48, 88, 256, 1024, 344, 136, 136, 344, 1024, 4096, 1368, 480, 272, 480, 1368, 4096, 16384, 5464, 1848, 752, 752, 1848, 5464, 16384, 65536, 21848, 7312, 2600, 1504, 2600, 7312, 21848, 65536, 262144, 87384, 29160

Offset: 0

Author

T. D. Noe, Aug 06 2013

Keywords

• nonn
• tabl

Comments

All rows except the zeroth are divisible by 4. Is there a closed-form formula for these numbers, like for binomial coefficients?

Examples

			Triangle begins:
  1,
  4, 4,
  16, 8, 16,
  64, 24, 24, 64,
  256, 88, 48, 88, 256,
  1024, 344, 136, 136, 344, 1024,
  4096, 1368, 480, 272, 480, 1368, 4096,
  16384, 5464, 1848, 752, 752, 1848, 5464, 16384,
  65536, 21848, 7312, 2600, 1504, 2600, 7312, 21848, 65536
		

Links

• T. D. Noe, Rows n = 0..50 of triangle, flattened

Crossrefs

Cf. A007318 (Pascal's triangle), A228053 ((-1)^n on the borders).

Cf. A051601 (n on the borders), A137688 (2^n on borders).

Cf. A165665 (row sums: 3*4^n - 2*2^n), A227075 (3^n edges), A227076 (5^n edges).

Programs

Mathematica

t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = 4^n, m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t = Flatten[t]