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A227075 A triangle formed like Pascal's triangle, but with 3^n on the borders instead of 1. 6
1, 3, 3, 9, 6, 9, 27, 15, 15, 27, 81, 42, 30, 42, 81, 243, 123, 72, 72, 123, 243, 729, 366, 195, 144, 195, 366, 729, 2187, 1095, 561, 339, 339, 561, 1095, 2187, 6561, 3282, 1656, 900, 678, 900, 1656, 3282, 6561, 19683, 9843, 4938, 2556, 1578, 1578, 2556, 4938 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All rows except the zeroth are divisible by 3. Is there a closed-form formula for these numbers, like for binomial coefficients?

Let b=3 and T(n,k) = A(n-k,k) be the associated reading of the symmetric array A by antidiagonals, then A(n,k) = sum_{r=1..n} b^r*A178300(n-r,k) + sum_{c=1..k} b^c*A178300(k-c,n). Similarly with b=4 and b=5 for A227074 and A227076. - R. J. Mathar, Aug 10 2013

LINKS

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

EXAMPLE

Triangle:

1,

3, 3,

9, 6, 9,

27, 15, 15, 27,

81, 42, 30, 42, 81,

243, 123, 72, 72, 123, 243,

729, 366, 195, 144, 195, 366, 729,

2187, 1095, 561, 339, 339, 561, 1095, 2187,

6561, 3282, 1656, 900, 678, 900, 1656, 3282, 6561

MATHEMATICA

t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = 3^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. A166060 (row sums: 4*3^n - 3*2^n), A227074 (4^n edges), A227076 (5^n edges).

Sequence in context: A197414 A247571 A292885 * A165351 A215665 A200494

Adjacent sequences:  A227072 A227073 A227074 * A227076 A227077 A227078

KEYWORD

nonn,tabl

AUTHOR

T. D. Noe, Aug 01 2013

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)