A123486 Riordan array (1/(1-2*x), x/(1-4*x^2)).
1, 2, 1, 4, 2, 1, 8, 8, 2, 1, 16, 16, 12, 2, 1, 32, 48, 24, 16, 2, 1, 64, 96, 96, 32, 20, 2, 1, 128, 256, 192, 160, 40, 24, 2, 1, 256, 512, 640, 320, 240, 48, 28, 2, 1, 512, 1280, 1280, 1280, 480, 336, 56, 32, 2, 1, 1024, 2560, 3840, 2560, 2240, 672, 448, 64, 36, 2, 1
Offset: 0
Examples
Number triangle begins 1; 2, 1; 4, 2, 1; 8, 8, 2, 1; 16, 16, 12, 2, 1; 32, 48, 24, 16, 2, 1;
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Programs
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Mathematica
Table[Binomial[Floor[(n + k)/2], k]*2^(n - k), {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 13 2017 *) -
PARI
for(n=0,10, for(k=0,n, print1(binomial(floor((n+k)/2),k)*2^(n-k), ", "))) \\ G. C. Greubel, Oct 13 2017
Formula
Number triangle T(n,k) = C(floor((n+k)/2), k) * 2^(n-k).
T(n,k) = T(n-1,k-1) + 4*T(n-2,k), T(0,0) = 1, T(1,0) = 2, T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 20 2014
Extensions
Terms a(46) onward added by G. C. Greubel, Oct 14 2017
Comments