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A227074
A triangle formed like Pascal's triangle, but with 4^n on the borders instead of 1.
5
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
0,2
COMMENTS
All rows except the zeroth are divisible by 4. Is there a closed-form formula for these numbers, like for binomial coefficients?
EXAMPLE
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
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]
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).
Sequence in context: A079611 A246763 A319070 * A174595 A160020 A273370
KEYWORD
nonn,tabl
AUTHOR
T. D. Noe, Aug 06 2013
STATUS
approved