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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238303 Triangle T(n,k), 0<=k<=n, read by rows given by T(n,0) = 1, T(n,k) = 2 if k>0. 2
1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are A005408(n).

Diagonals sums are A109613(n).

Sum_{k=0..n} T(n,k)*x^k = A033999(n), A000012(n), A005408(n), A036563(n+2), A058481(n+1), A083584(n), A137410(n), A233325(n), A233326(n), A233328(n), A211866(n+1), A165402(n+1) for x = -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 respectively.

Sum_{k=0..n} T(n,k)*x^(n-k) = A151575(n), A000012(n), A040000(n), A005408(n), A033484(n), A048473(n), A020989(n), A057651(n), A061801(n), A238275(n), A238276(n), A138894(n), A090843(n), A199023(n) for x = -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 respectively.

Sum_{k=0..n} T(n,k)^x = A000027(n+1), A005408(n), A016813(n), A017077(n) for x = 0, 1, 2, 3 respectively.

Sum_{k=0..n} k*T(n,k) = A002378(n).

Sum_{k=0..n} A000045(k)*T(n,k) = A019274(n+2).

Sum_{k=0..n} A000142(k)*T(n,k) = A066237(n+1).

LINKS

Table of n, a(n) for n=0..85.

FORMULA

T(n,0) = A000012(n) = 1, T(n+k,k) = A007395(n) = 2 for k>0.

EXAMPLE

Triangle begins:

1;

1, 2;

1, 2, 2;

1, 2, 2, 2;

1, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2;

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2;

...

CROSSREFS

Cf. Diagonals: A040000.

Cf. Columns: A000012, A007395.

First differences of A001614.

Sequence in context: A274353 A183028 A114284 * A023575 A215113 A058978

Adjacent sequences: A238300 A238301 A238302 * A238304 A238305 A238306

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 24 2014

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 December 7 12:12 EST 2022. Contains 358656 sequences. (Running on oeis4.)