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A182436 Triangle T(n,k), read by rows, given by (2, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 0
1, 2, 1, 2, 5, 2, 4, 8, 11, 4, 4, 20, 25, 24, 8, 8, 28, 70, 69, 52, 16, 8, 60, 126, 213, 178, 112, 32, 16, 80, 288, 460, 599, 440, 240, 64, 16, 160, 472, 1128, 1489, 1600, 1056, 512, 128, 32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are the powers of 3.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

G.f.: (1+2*x-y*x)/(1-2*y*x-(2+y)*x^2).

T(n,k) = 2*T(n-1,k-1) + 2*T(n-2,k) + T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = T(2,0) = T(2,2) = 2, T(2,1) = 5 and T(n,k) = 0 if k<0 or if k>n.

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A123335(n-1), A016116(n+1), A000244(n), A057087(n), A091928(n) for x = -2, -1, 0, 1, 2, 3 respectively.

EXAMPLE

Triangle begins :

1

2, 1

2, 5, 2

4, 8, 11, 4

4, 20, 25, 24, 8

8, 28, 70, 69, 52, 16

8, 60, 126, 213, 178, 112, 32

16, 80, 288, 460, 599, 440, 240, 64

16, 160, 472, 1128, 1489, 1600, 1056, 512, 128

32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256

CROSSREFS

Cf. A016116, A011782, A111297, A000244

Sequence in context: A095149 A218579 A329198 * A064192 A284553 A216913

Adjacent sequences:  A182433 A182434 A182435 * A182437 A182438 A182439

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Apr 28 2012

STATUS

approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)