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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 Table of n, a(n) for n=1..58. 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 Adjacent sequences: A204201 A204202 A204203 * A204205 A204206 A204207 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.)