

A058394


A square array based on natural numbers (A000027) with each term being the sum of 2 consecutive terms in the previous row.


3



1, 0, 1, 2, 1, 1, 0, 2, 2, 1, 3, 2, 3, 3, 1, 0, 3, 4, 5, 4, 1, 4, 3, 5, 7, 8, 5, 1, 0, 4, 6, 9, 12, 12, 6, 1, 5, 4, 7, 11, 16, 20, 17, 7, 1, 0, 5, 8, 13, 20, 28, 32, 23, 8, 1, 6, 5, 9, 15, 24, 36, 48, 49, 30, 9, 1, 0, 6, 10, 17, 28, 44, 64, 80, 72, 38, 10, 1, 7, 6, 11, 19, 32, 52, 80, 112, 129
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OFFSET

0,4


COMMENTS

Changing the formula by replacing T(2n,0)=T(n,2) by T(2n,0)=T(n,m) for some other value of m, would make the generating function change to coefficient of x^n in expansion of (1+x)^k/(1x^2)^m. This would produce A058393, A058395, A057884 (and effectively A007318).


LINKS

Table of n, a(n) for n=0..86.


FORMULA

T(n, k)=T(n1, k1)+T(n, k1) with T(0, k)=1, T(2n, 0)=T(n, 2) and T(2n+1, 0)=0. Coefficient of x^n in expansion of (1+x)^k/(1x^2)^2.


EXAMPLE

Rows are (1,0,2,0,3,0,4,...), (1,1,2,2,3,3,...), (1,2,3,4,5,6,...), (1,3,5,7,9,11,...), etc.


CROSSREFS

Rows are A027656 (A000027 with zeros), A008619, A000027, A005408, A008574 etc. Columns are A000012, A001477, A022856 etc. Diagonals include A034007, A045891, A045623, A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055251 etc. The triangle A055249 also appears in half of the array.
Sequence in context: A025860 A322285 A152487 * A122860 A113661 A113974
Adjacent sequences: A058391 A058392 A058393 * A058395 A058396 A058397


KEYWORD

nonn,tabl


AUTHOR

Henry Bottomley, Nov 24 2000


STATUS

approved



