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A271355 Triangular array:  T(n,k) = |round[(r^n)*(s^k)|, where r = golden ratio = (1+ sqrt(5))/2, s = (1 - sqrt(5))/2, 1 < = k <= n, n > = 0. 2
1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 7, 4, 3, 2, 1, 11, 7, 4, 3, 2, 1, 18, 11, 7, 4, 3, 2, 1, 29, 18, 11, 7, 4, 3, 2, 1, 47, 29, 18, 11, 7, 4, 3, 2, 1, 76, 47, 29, 18, 11, 7, 4, 3, 2, 1, 123, 76, 47, 29, 18, 11, 7, 4, 3, 2, 1, 199, 123, 76, 47, 29, 18, 11, 7, 4, 3 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n consists of the first n numbers of A169985 = (1,2,3,4,7,... ) in reverse order; these are the Lucas numbers, A000032, with order of initial two terms reversed.  Every column of the triangle is A169985.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

FORMULA

T(n,k) = |round[(r^n)*(s^k)|, where r = golden ratio = (1+ sqrt(5))/2, s = (1 - sqrt(5))/2, 1 < = k <= n, n > = 0.

T(k+j-1,j) = A000032(k) = k-th Lucas number, for k >= 2.

EXAMPLE

First six rows:

1

2   1

3   2   1

4   3   2   1

7   4   3   2   1

11  7   4   3   2   1

MATHEMATICA

r = N[(1 + Sqrt[5])/2, 100]; s = N[(1 - Sqrt[5])/2, 100];

t = Table[Abs[Round[(r^n)*(s^k)]], {n, 0, 15}, {k, 1, n}];

Flatten[t]  (* A271355, sequence *)

TableForm[t]  (* A271355, array *)

CROSSREFS

Cf. A169985, A000032, A000045, A104762

Sequence in context: A200082 A052310 A052313 * A211230 A049085 A193173

Adjacent sequences:  A271352 A271353 A271354 * A271356 A271357 A271358

KEYWORD

nonn,easy,tabl

AUTHOR

Clark Kimberling, May 01 2016

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)