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A204207 Triangle based on (1,2,3) averaging array. 2
2, 3, 5, 5, 8, 11, 9, 13, 19, 23, 17, 22, 32, 42, 47, 33, 39, 54, 74, 89, 95, 65, 72, 93, 128, 163, 184, 191, 129, 137, 165, 221, 291, 347, 375, 383, 257, 266, 302, 386, 512, 638, 722, 758, 767, 513, 523, 568, 688, 898, 1150, 1360, 1480, 1525, 1535, 1025 (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..56.

FORMULA

T(n,n) = A083329(n). - Philippe Deléham, Dec 24 2013

T(n,1) = A000051(n-1). - Philippe Deléham, Dec 24 2013

Sum_{k=1..n} T(n,k)=A036289(n). - Philippe Deléham, Dec 24 2013

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)=2, T(2,1)=3, T(2,2)=5, T(n,k)=0 if k<1 or if k>n. - Philippe Deléham, Dec 24 2013

EXAMPLE

First six rows:

2

3....5

5....8....11

9....13...19...23

17...22...32...42...47

33...39...54...74...89...95

MATHEMATICA

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

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[2 (1/2) (1/r) 2^n*u[n], {n, 1, 12}];

TableForm[u] (* A204207 triangle *)

Flatten[u]   (* A204207 sequence *)

CROSSREFS

Cf. A204201.

Sequence in context: A194939 A135635 A238007 * A287919 A138181 A006447

Adjacent sequences:  A204204 A204205 A204206 * A204208 A204209 A204210

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

EXTENSIONS

Example corrected by Philippe Deléham, Dec 22 2013

STATUS

approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)