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A204203 Triangle based on (0,1/4,1) averaging array. 2
1, 1, 5, 1, 6, 13, 1, 7, 19, 29, 1, 8, 26, 48, 61, 1, 9, 34, 74, 109, 125, 1, 10, 43, 108, 183, 234, 253, 1, 11, 53, 151, 291, 417, 487, 509, 1, 12, 64, 204, 442, 708, 904, 996, 1021, 1, 13, 76, 268, 646, 1150, 1612, 1900, 2017, 2045, 1, 14, 89, 344, 914 (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..60.

FORMULA

From Philippe Deléham, Dec 24 2013: (Start)

T(n,n) = A036563(n+1).

Sum_{k=1..n} T(n,k) = A014480(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)=1, T(2,1)=1, T(2,2)=5, T(n,k)=0 if k<1 or if k>n. (End)

EXAMPLE

First six rows:

1

1...5

1...6...13

1...7...19...29

1...8...26...48...61

1...9...34...74...109...125

MATHEMATICA

a = 0; r = 1/4; 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[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];

TableForm[u]  (* A204203 triangle *)

Flatten[u]    (* A204203 sequence *)

CROSSREFS

Cf. A204201.

Sequence in context: A160824 A193586 A007397 * A261721 A275490 A052345

Adjacent sequences:  A204200 A204201 A204202 * A204204 A204205 A204206

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)