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A114164 Riordan array (1/(1-2x), x(1-x)/(1-2x)^2). 3
1, 2, 1, 4, 5, 1, 8, 18, 8, 1, 16, 56, 41, 11, 1, 32, 160, 170, 73, 14, 1, 64, 432, 620, 377, 114, 17, 1, 128, 1120, 2072, 1666, 704, 164, 20, 1, 256, 2816, 6496, 6608, 3649, 1178, 223, 23, 1, 512, 6912, 19392, 24192, 16722, 7001, 1826, 291, 26, 1, 1024, 16640 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A081567. Diagonal sums are A085810. Product of Pascal triangle A007318 and Morgan-Voyce triangle A085478.

Unsigned version of A123876. - Philippe Deléham, Oct 25 2007

LINKS

Table of n, a(n) for n=0..56.

FORMULA

Number triangle T(n,k) = Sum_{j=0..n} C(n, j)*C(j+k, 2k);

T(n,k) = Sum_{j=0..n} C(n, k+j)*C(k, k-j)*2^(n-k-j)};

T(n, k) = Sum_{j=0..n-k} C(n+k-j, n-k-j)*C(k, j)*(-1)^j*2^(n-k-j).

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Jan 17 2014

EXAMPLE

Triangle begins

   1;

   2,   1;

   4,   5,   1;

   8,  18,   8,  1;

  16,  56,  41, 11,  1;

  32, 160, 170, 73, 14, 1;

CROSSREFS

Sequence in context: A117317 A124237 A123876 * A176667 A126182 A154342

Adjacent sequences:  A114161 A114162 A114163 * A114165 A114166 A114167

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 15 2005

STATUS

approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)