login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103525 Triangle read by rows: T(n,k) is the coefficient of t^k (k>=0) in the polynomial P[n,t] defined by P[1,t] = P[2,t] = 1, P[3,t] = 1+t, P[n,t] = P[n-1,t] + P^2[n-2,1] for n >= 4. 0
1, 1, 1, 1, 2, 1, 3, 3, 1, 7, 7, 2, 16, 25, 17, 6, 1, 65, 123, 94, 34, 5, 321, 923, 1263, 1076, 626, 254, 70, 12, 1, 4546, 16913, 28612, 28620, 18476, 7876, 2166, 352, 26, 107587, 609479, 1691387, 3050910, 4001833, 4044516, 3255042, 2126032, 1138124, 500806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

T(n,k) is the number of certain types of trees (see the Duke et al. reference) of height n and having k branch nodes at level n-1. Row n has 2^(ceiling(n/2)-2)+1 terms (n >= 3). Row sums yield A000278. T(n,0) = A000278(n-1) for n >= 2.

LINKS

Table of n, a(n) for n=1..50.

W. Duke, Stephen J. Greenfield and Eugene R. Speer, Properties of a Quadratic Fibonacci Recurrence, J. Integer Sequences, 1998, #98.1.8.

FORMULA

T(1,0)=1; T(2,0)=1; T(3,0)=T(3,1)=1; T(n,k)=0 for k >= ceiling(n/2); T(n,k) = T(n-1, k) + Sum_{j=0..k} T(n-2, j)*T(n-2, k-j) for n >= 4.

EXAMPLE

P[5,t] = 3 + 3*t + t^2; therefore T(3,0)=3, T(3,1)=3, T(3,2)=1.

Triangle begins:

   1;

   1;

   1,  1;

   2,  1;

   3,  3,  1;

   7,  7,  2;

  16, 25, 17,  6,  1;

MAPLE

P[1]:=1:P[2]:=1:P[3]:=1+t:for n from 4 to 13 do P[n]:=sort(expand(P[n-1]+P[n-2]^2)) od:for n from 1 to 11 do seq(coeff(t*P[n], t^k), k=1..2^(ceil(n/2)-2)+1) od; # yields sequence in triangular form

CROSSREFS

Cf. A000278.

Sequence in context: A127123 A271238 A186740 * A294432 A121436 A330694

Adjacent sequences:  A103522 A103523 A103524 * A103526 A103527 A103528

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Mar 21 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)