login
This site is supported by donations to The OEIS Foundation.

 

Logo

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!)
A007466 Exponential-convolution of natural numbers with themselves.
(Formerly M3478)
6
1, 4, 14, 44, 128, 352, 928, 2368, 5888, 14336, 34304, 80896, 188416, 434176, 991232, 2244608, 5046272, 11272192, 25034752, 55312384, 121634816, 266338304, 580911104, 1262485504, 2734686208, 5905580032, 12717129728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Define a triangle T by T(n,1) = n*(n-1)+1 and T(r,c) = T(r,c-1) + T(r-1,c-1), then a(n) = T(n,n). - J. M. Bergot, Mar 03 2013

This is triangle A228643: a(n) = A228643(n,n). - Aug 29 2013

With offset 0, a(n) is the number of 2 X n 0-1 matrices that do not contain, as a 2 X 2 submatrix,

  1 1 or 0 0

  0 0 .. 1 1.

(See Ju and Seo link, Theorem 3.2.) - David Callan, Jul 11 2014

a(n) = the sum of all ways of adding the k-tuples of the terms in the (n-1)-st row of Pascal's triangle A007318. For n=4 take row 3 of A007318: 1,3,3,1, giving (1)+(3)+(3)+(1)=8; (1+3)+(3+3)+(3+1)=14; (1+3+3)+(3+3+1)=14; (1+3+3+1)=8. The sum of these four terms is 8+14+14+8=44. - J. M. Bergot, Jun 17 2017

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Hyeong-Kwan Ju and Seunghyun Seo, Enumeration of 0/1-matrices avoiding some 2x2 matrices, arXiv:1107.1299 [math.CO], 2011.

Hyeong-Kwan Ju and Seunghyun Seo, Enumeration of (0,1)-matrices avoiding some 2 X 2 matrices, Discrete Math., 312 (2012), 2473-2481.

N. J. A. Sloane, Transforms

Index entries for linear recurrences with constant coefficients, signature (6,-12,8)

FORMULA

E.g.f.: (Sum_{n >= 1} n*x^(n-1)/(n-1)!)^2.

a(n) = 2^(n-1)*n+1/4*2^(n-1)*(n-1)*(n-2).

a(n) = Sum_{k=0..(n+2)} C(n+2, k) * floor(k/2)^2. - Paul Barry, Mar 06 2003

E.g.f.: (1+x)^2*exp(2*x). - Vladeta Jovovic, Sep 09 2003

G.f.: -(2*x^3-2*x^2+x)/(2*x-1)^3. - Vladimir Kruchinin, Sep 28 2011

E.g.f.: U(0) where U(k)= 1 + 2*x/( 1 - x/(2 + x - 4/( 2 + x*(k+1)/U(k+1)))) ; (continued fraction, 3rd kind, 4-step). - Sergei N. Gladkovskii, Oct 28 2012

MAPLE

A007466:=n->2^(n-1)*n+1/4*2^(n-1)*(n-1)*(n-2): seq(A007466(n), n=1..30);

MATHEMATICA

Table[2^(n - 1)*n + 1/4*2^(n - 1)*(n - 1)*(n - 2), {n, 30}] (* Wesley Ivan Hurt, Jul 11 2014 *)

PROG

(Haskell)

a007466 n = a228643 n n  -- Reinhard Zumkeller, Aug 29 2013

(MAGMA) [2^(n-1)*n+1/4*2^(n-1)*(n-1)*(n-2) : n in [1..30]]; // Wesley Ivan Hurt, Jul 11 2014

CROSSREFS

Sequence in context: A084613 A099063 A057223 * A062109 A118042 A006645

Adjacent sequences:  A007463 A007464 A007465 * A007467 A007468 A007469

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

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 December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)