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A204206 Triangle based on (1,3/2,2) averaging array. 2
3, 5, 7, 9, 12, 15, 17, 21, 27, 31, 33, 38, 48, 58, 63, 65, 71, 86, 106, 121, 127, 129, 136, 157, 192, 227, 248, 255, 257, 265, 293, 349, 419, 475, 503, 511, 513, 522, 558, 642, 768, 894, 978, 1014, 1023, 1025, 1035, 1080, 1200, 1410, 1662, 1872 (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..52.

FORMULA

From Philippe Deléham, Dec 24 2013: (Start)

T(n,n) = A000225(n+1).

Sum_{k=1..n} T(n,k) = A167667(n).

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)=5, T(2,2)=7, T(n,k)=0 if k<1 or if k>n. (End)

EXAMPLE

First six rows:

3

5...7

9...12...15

17..21...27...31

33..38...48...58...63

65..71...86...106..121..127

MATHEMATICA

a = 1; r = 3/2; b = 2;

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]   (* A204206 triangle *)

Flatten[u]     (* A204206 sequence *)

CROSSREFS

Cf. A204201.

Sequence in context: A186705 A072154 A309269 * A080751 A025218 A258782

Adjacent sequences:  A204203 A204204 A204205 * A204207 A204208 A204209

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)