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A204205 Triangle based on (0,1/5,1) averaging array. 2
1, 1, 6, 1, 7, 16, 1, 8, 23, 36, 1, 9, 31, 59, 76, 1, 10, 40, 90, 135, 156, 1, 11, 50, 130, 225, 291, 316, 1, 12, 61, 180, 355, 516, 607, 636, 1, 13, 73, 241, 535, 871, 1123, 1243, 1276, 1, 14, 86, 314, 776, 1406, 1994, 2366, 2519, 2556, 1, 15, 100, 400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A204201 for a discussion and guide to other averaging arrays.

LINKS

Table of n, a(n) for n=1..59.

FORMULA

T(n,n) = A048487(n-1). - 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)=1, T(2,1)=1, T(2,2)=6, T(n,k)=0 if k<1 or if k>n. - Philippe Deléham, Dec 24 2013

EXAMPLE

First six rows:

1

1...6

1...7...16

1...8...23...36

1...9...31...59...76

1...10..40...90...135...156

MATHEMATICA

a = 0; r = 1/5; 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[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];

TableForm[u]   (* A204205 triangle *)

Flatten[u]     (* A204205 sequence *)

CROSSREFS

Cf. A204201.

Sequence in context: A082830 A261622 A046902 * A143019 A156921 A094214

Adjacent sequences:  A204202 A204203 A204204 * A204206 A204207 A204208

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)