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A216344 Triangle T(n,k), read by rows, given by (0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, -1, 1, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938 . 0
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 4, 3, 1, 0, 8, 8, 7, 4, 1, 0, 16, 16, 16, 11, 5, 1, 0, 32, 32, 36, 28, 16, 6, 1, 0, 64, 64, 80, 68, 45, 22, 7, 1, 0, 128, 128, 176, 160, 118, 68, 29, 8, 1, 0, 256, 256, 384 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..58.

FORMULA

G.f.: (1-2*x+y*x^2)/(1-2*x-y*x+2*y*x^2-y^2*x^3)

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,1) = T(2,1) = T(2,2) = 1, T(1,0) = T(2,0) = 0 and T(n,k) = 0 if k<0 or if k>n .

Sum_{k, 0<=k<=n} T(n,k) = A034943(n+1) .

Sum_{k, 0<=k<=n} T(n,k)*2^k*(-1/2)^(n-k) = A052955(n) .

T(n+1,1) = A011782(n), T(n+2,2) = 2^n = A000079(n), T(n+3,3) = A045891(n+1) .

EXAMPLE

Triangle begins :

1

0, 1

0, 1, 1

0, 2, 2, 1

0, 4, 4, 3, 1

0, 8, 8, 7, 4, 1

0, 16, 16, 16, 11, 5, 1

0, 32, 32, 36, 28, 16, 6, 1

CROSSREFS

Cf. A034943

Sequence in context: A071510 A110124 A116389 * A332011 A229762 A062110

Adjacent sequences:  A216341 A216342 A216343 * A216345 A216346 A216347

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Sep 04 2012

STATUS

approved

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Last modified June 27 23:49 EDT 2022. Contains 354903 sequences. (Running on oeis4.)