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A030111 Triangular array in which k-th entry in n-th row is C([ (n+k)/2 ],k) (1<=k<=n). 4
1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 3, 4, 1, 1, 3, 6, 4, 5, 1, 1, 4, 6, 10, 5, 6, 1, 1, 4, 10, 10, 15, 6, 7, 1, 1, 5, 10, 20, 15, 21, 7, 8, 1, 1, 5, 15, 20, 35, 21, 28, 8, 9, 1, 1, 6, 15, 35, 35, 56, 28, 36, 9, 10, 1, 1, 6, 21, 35, 70, 56, 84, 36, 45, 10, 11, 1, 1, 7, 21, 56, 70, 126, 84, 120, 45, 55, 11, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Same as A046854, but missing the initial column of ones.

Riordan array (1/((1-x)(1-x^2)),x/(1-x^2)). Diagonal sums are A052551. - Paul Barry, Sep 30 2006

LINKS

Indranil Ghosh, Rows 0..125, flattened

FORMULA

G.f.: 1 / (1 - x - xy - x^2 + x^2y + x^3). - Ralf Stephan, Feb 13 2005

Sum(k=1, n, T(n, k)) = F(n+2)-1 where F(n) is the n-th Fibonacci number. - Benoit Cloitre, Oct 07 2002

EXAMPLE

1;

1 1;

2 1 1;

2 3 1 1;

3 3 4 1 1;

3 6 4 5 1 1;

...

MATHEMATICA

Flatten[Table[Binomial[Floor[(n+k)/2], k], {n, 20}, {k, n}]] (* Harvey P. Dale, Jun 03 2014 *)

PROG

(PARI) {T(n, k) = binomial((n+k)\2, k)}; /* Michael Somos, Jul 23 1999 */

(PARI) printp(matrix(8, 8, n, k, binomial((n+k)\2, k)))

(PARI) for(n=1, 7, for(k=1, n, print1(binomial((n+k)\2, k)); if(k==n, print1("; ")); print1(" ")))

CROSSREFS

Cf. A066170.

Sequence in context: A116855 A173265 A157744 * A096921 A275416 A037161

Adjacent sequences:  A030108 A030109 A030110 * A030112 A030113 A030114

KEYWORD

tabl,nonn

AUTHOR

Jacques Haubrich (jhaubrich(AT)freeler.nl)

EXTENSIONS

Description corrected by Michael Somos, Jul 23 1999

Corrected and extended by Harvey P. Dale, Jun 03 2014

STATUS

approved

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Last modified June 24 07:19 EDT 2017. Contains 288697 sequences.