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A204204 Triangle based on (0,3/4,1) averaging array. 2
3, 3, 7, 3, 10, 15, 3, 13, 25, 31, 3, 16, 38, 56, 63, 3, 19, 54, 94, 119, 127, 3, 22, 73, 148, 213, 246, 255, 3, 25, 95, 221, 361, 459, 501, 511, 3, 28, 120, 316, 582, 820, 960, 1012, 1023, 3, 31, 148, 436, 898, 1402, 1780, 1972, 2035, 2047, 3, 34, 179 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A204201 for a discussion and guide to other averaging arrays.
LINKS
FORMULA
From Philippe Deléham, Dec 24 2013: (Start)
T(n,n) = A000225(n+1).
Sum_{k=1..n} T(n,k) = A128135(n+1).
T(n,k)=T(n-1,k)+3*T(n-1,k-1)-2*T(n-2,k-1)-2*T(n-2,k-2), T(1,1)=3, T(2,1)=3, T(2,2)=7, T(n,k)=0 if k<1 or if k>n. (End)
EXAMPLE
First six rows:
3
3...7
3...10...15
3...13...25...31
3...16...38...56...63
3...19...54...94...119..127
MATHEMATICA
a = 0; r = 3/4; b = 1;
t[1, 1] = r;
t[n_, 1] := (a + t[n - 1, 1])/2;
t[n_, n_] := (b + t[n - 1, n - 1])/2;
t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
u[n_] := Table[t[n, k], {k, 1, n}]
Table[u[n], {n, 1, 5}] (* averaging array *)
u = Table[3 (1/2) (1/r) 2^n*u[n], {n, 1, 12}];
TableForm[u] (* A204204 triangle *)
Flatten[u] (* A204204 sequence *)
CROSSREFS
Cf. A204201.
Sequence in context: A092693 A134661 A135434 * A164928 A253249 A069949
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 12 2012
STATUS
approved

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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)