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!)
A241862 Number of compositions of n such that the smallest part has multiplicity two. 3
1, 0, 4, 3, 10, 18, 35, 60, 121, 217, 391, 709, 1281, 2283, 4061, 7185, 12680, 22291, 39051, 68191, 118767, 206331, 357596, 618345, 1066983, 1837513, 3158685, 5420335, 9286086, 15884155, 27130404, 46274560, 78822938, 134095757, 227853408, 386721362, 655639944 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 2..1000
FORMULA
a(n) ~ (1/4 - 11/(20*sqrt(5))) * n^2 * ((1+sqrt(5))/2)^n. - Vaclav Kotesovec, May 01 2014
Equivalently, a(n) ~ n^2 * phi^(n-5) / (2 * 5^(3/2)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Dec 06 2021
MAPLE
b:= proc(n, s) option remember; `if`(n=0, 1,
`if`(n<s, 0, expand(add(b(n-j, s)*x, j=s..n))))
end:
a:= proc(n) local k; k:= 2;
add((p->add(coeff(p, x, i)*binomial(i+k, k),
i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k)
end:
seq(a(n), n=2..40);
MATHEMATICA
b[n_, s_] := b[n, s] = If[n == 0, 1, If[n<s, 0, Expand[Sum[b[n-j, s]*x, {j, s, n}]]]]; a[n_] := With[{k=2}, Sum[Function[{p}, Sum[Coefficient[p, x, i]*Binomial[i+k, k], {i, 0, Exponent[p, x]}]][b[n-j*k, j+1]], {j, 1, n/k}]]; Table[a[n], {n, 2, 40}] (* Jean-François Alcover, Nov 07 2014, after Maple *)
CROSSREFS
Column k=2 of A238342.
Cf. A001622.
Sequence in context: A185730 A205965 A242391 * A222510 A100492 A072183
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Apr 30 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 July 19 04:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)