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A208324 Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -2, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 0
1, 2, 4, 3, 10, 8, 4, 18, 28, 16, 5, 28, 64, 72, 32, 6, 40, 120, 200, 176, 64, 7, 54, 200, 440, 576, 416, 128, 8, 70, 308, 840, 1456, 1568, 960, 256, 9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums are A134931(n).
Diagonal sums are A140253(n).
Compare this sequence with A207627.
Column k is divisible by 2^k.
LINKS
FORMULA
T(n,0) = n+1.
T(n,1) = 2*T(n,0) + T(n-1,1).
T(n,k) = 2*T(n-1,k-1) + T(n-1,k) for k>1.
T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) with T(0,0) = 1, T(1,0) = 2, T(1,1) = 4.
G.f.: (1+2*y*x)/(1-2*(1+y)*x+(1+2*y)*x^2).
EXAMPLE
Triangle begins :
1
2, 4
3, 10, 8
4, 18, 28, 16
5, 28, 64, 72, 32
6, 40, 120, 200, 176, 64
7, 54, 200, 440, 576, 416, 128
8, 70, 308, 840, 1456, 1568, 960, 256
9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512
10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864, 1024
CROSSREFS
Sequence in context: A226367 A324934 A240271 * A277416 A064691 A247071
KEYWORD
easy,nonn,tabl
AUTHOR
Philippe Deléham, Feb 25 2012
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)