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A099573 Reverse of number triangle A054450. 1
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 5, 1, 1, 5, 5, 8, 8, 1, 1, 6, 6, 12, 12, 13, 1, 1, 7, 7, 17, 17, 21, 21, 1, 1, 8, 8, 23, 23, 33, 33, 34, 1, 1, 9, 9, 30, 30, 50, 50, 55, 55, 1, 1, 10, 10, 38, 38, 73, 73, 88, 88, 89, 1, 1, 11, 11, 47, 47, 103, 103, 138, 138, 144, 144, 1, 1, 12, 12, 57 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are A029907(n+1). Diagonal sums are A099574. Diagonal is A000045(n+1).

LINKS

Table of n, a(n) for n=0..82.

FORMULA

Number triangle T(n, k)=if(k<=n, sum{j=0..floor(k/2), binomial(n-j, j)}, 0).

Antidiagonals of the following array: the first row equals the Fibonacci numbers, (1, 1, 2, 3, 5,...), and the (n+1)-st row is obtained by the matrix-vector product A128174 * n-th row. - Gary W. Adamson, Jan 19 2011

EXAMPLE

Rows of the triangle start {1}, {1,1}, {1,1,2}, {1,1,3,3}, {1,1,4,4,5},...

First few rows of the array are:

1, 1, 2, 3,. 5, .8,... A000045

1, 1, 3, 4,. 8, 12,... A052952

1, 1, 4, 5,.12, 17,... A054451

1, 1, 5, 6,.17, 23,... A099571

1, 1, 6, 7,.23, 30,... A099572

...

CROSSREFS

Cf. A099575, A054450.

Sequence in context: A049695 A096589 A176427 * A107430 A255741 A132892

Adjacent sequences:  A099570 A099571 A099572 * A099574 A099575 A099576

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 23 2004

STATUS

approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)