A115284 - OEIS

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A115284

Correlation triangle of 4-C(1,n)-2*C(0,n) (A113311).

1, 3, 3, 4, 10, 4, 4, 15, 15, 4, 4, 16, 26, 16, 4, 4, 16, 31, 31, 16, 4, 4, 16, 32, 42, 32, 16, 4, 4, 16, 32, 47, 47, 32, 16, 4, 4, 16, 32, 48, 58, 48, 32, 16, 4, 4, 16, 32, 48, 63, 63, 48, 32, 16, 4, 4, 16, 32, 48, 64, 74, 64, 48, 32, 16, 4

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Row sums are the coordination sequence for cubic lattice A005899. Diagonal sums are A115285. T(2n,n) is A113770. T(2n,n)-T(2n,n+1) is 1,6,10,10,10,.... (10-4C(1,n)-5C(0,n)).

LINKS

Table of n, a(n) for n=0..65.

FORMULA

G.f.: (1+x)^2*(1+x*y)^2/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*(4-C(1, k-j)-2C(0, k-j))*[j<=n-k]*((4-C(1, n-k-j)-2C(0, n-k-j))}.

EXAMPLE

Triangle begins

3, 3;

4, 10, 4;

4, 15, 15, 4;

4, 16, 26, 16, 4;

4, 16, 31, 31, 16, 4;

4, 16, 32, 42, 32, 16, 4;

CROSSREFS

Sequence in context: A132319 A130626 A175796 * A202869 A202871 A368224

Adjacent sequences: A115281 A115282 A115283 * A115285 A115286 A115287

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 19 2006

STATUS

approved