This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A105477 Triangle read by rows: T(n,k) is the number of compositions of n into k parts when there are two kinds of part 2. 2
 1, 2, 1, 1, 4, 1, 1, 6, 6, 1, 1, 6, 15, 8, 1, 1, 7, 23, 28, 10, 1, 1, 8, 30, 60, 45, 12, 1, 1, 9, 39, 98, 125, 66, 14, 1, 1, 10, 49, 144, 255, 226, 91, 16, 1, 1, 11, 60, 202, 437, 561, 371, 120, 18, 1, 1, 12, 72, 272, 685, 1128, 1092, 568, 153, 20, 1, 1, 13, 85, 355, 1015, 1995, 2555 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Triangle T(n,k), 1<=k<=n, given by (0, 2, -3/2, -1/6, 2/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Triangle T(n,k), 0<=k<=n, is the Riordan array (1, x*(1+x-x^2)/(1-x)) . - Philippe Deléham, Jan 25 2012 LINKS FORMULA G.f.=tz(1+z-z^2)/(1-z-tz-tz^2+tz^3). T(n,k)=Sum(binomial(k,j)*binomial(n-2j-1, k-j-1), j=0..n-k). - Emeric Deutsch, Aug 06 2006 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) - T(n-3,k-1), n>1. - Philippe Deléham, Jan 25 2012 EXAMPLE T(4,2)=6 because we have (1,3),(3,1),(2,2),(2,2'),(2',2) and (2',2'). Triangle begins: 1; 2,1; 1,4,1; 1,6,6,1; 1,6,15,8,1; Triangle T(n,k) given by (0,2,-3/2,-1/6,2/3,0,0,0,...) DELTA (1,0,0,0,0,...) begins : 1 0, 1 0, 2, 1 0, 1, 4, 1 0, 1, 6, 6, 1 0, 1, 6, 15, 8, 1... MAPLE G:=t*z*(1+z-z^2)/(1-z-t*z-t*z^2+t*z^3): Gser:=simplify(series(G, z=0, 15)): for n from 1 to 14 do P[n]:=coeff(Gser, z^n) od: for n from 1 to 13 do seq(coeff(P[n], t^k), k=1..n) od; # yields sequence in triangular form CROSSREFS Row sums yield A077998. Diagonals : A000012, A005843, A000384 Sequence in context: A122578 A208648 A005131 * A325772 A226174 A208482 Adjacent sequences:  A105474 A105475 A105476 * A105478 A105479 A105480 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Apr 09 2005 STATUS approved

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

Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)