login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A199478 Irregular triangle read by rows: T(n,i) = 2^(i-1)*(binomial(n-i+1,i)+binomial(n-i,i)), n >= 1, 0 <= i <= (n+1)/2. 1
1, 1, 1, 3, 1, 5, 2, 1, 7, 8, 1, 9, 18, 4, 1, 11, 32, 20, 1, 13, 50, 56, 8, 1, 15, 72, 120, 48, 1, 17, 98, 220, 160, 16, 1, 19, 128, 364, 400, 112, 1, 21, 162, 560, 840, 432, 32, 1, 23, 200, 816, 1568, 1232, 256, 1, 25, 242, 1140, 2688, 2912, 1120, 64, 1, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are 2^n. T(n,k) is the number of n-letter words from alphabet {a,b,c} not starting with a, having no consecutive letters and exactly k b's. - David Scambler, Dec 10 2011

LINKS

G. C. Greubel, Rows n=1..100 of triangle, flattened

Eddie Cheng, Ke Qiu and Zhizhang Shen, On the surface area of the augmented cubes, J. of Supercomputing, DOI: 10.1007/s11227-011-0641-1

EXAMPLE

Irregular triangle begins :

1, 1

1, 3

1, 5, 2

1, 7, 8

1, 9, 18, 4

1, 11, 32, 20

1, 13, 50, 56, 8

1, 15, 72, 120, 48

1, 17, 98, 220, 160, 16

1, 19, 128, 364, 400, 112

For n=2 one word has no b: ca, and three words have one b: ba, bc, cb.

MAPLE

scan3:=proc(a, M1) local lis, n, k;

lis:=[];

for n from 1 to M1 do for k from 0 to floor((n+1)/2) do

lis:=[op(lis), a(n, k)];

od: od:

lis;

end:

a:=(n, i)-> if i=0 then 1 else 2^(i-1)*(binomial(n-i+1, i)+binomial(n-i, i)); fi;

scan3(a, 15);

MATHEMATICA

T[ n_, k_] := Sum[ Binomial[ n - k, i - k] Binomial[ n - i + 1, 2 k - i], {i, 0, n}]; (* Michael Somos, Sep 20 2014 *)

PROG

(PARI) {T(n, k) = sum(i=0, n, binomial( n-k, i-k) * binomial( n-i+1, 2*k-i))}; /* Michael Somos, Sep 20 2014 */

CROSSREFS

Sequence in context: A130303 A100898 A101350 * A134867 A102573 A233940

Adjacent sequences: A199475 A199476 A199477 * A199479 A199480 A199481

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Nov 06 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 28 09:01 EST 2023. Contains 359851 sequences. (Running on oeis4.)