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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001648 Tetranacci numbers A073817 without the leading term 4.
(Formerly M2648 N1055)
14
1, 3, 7, 15, 26, 51, 99, 191, 367, 708, 1365, 2631, 5071, 9775, 18842, 36319, 70007, 134943, 260111, 501380, 966441, 1862875, 3590807, 6921503, 13341626, 25716811, 49570747, 95550687, 184179871, 355018116, 684319421, 1319068095, 2542585503, 4900991135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

LINKS

T. D. Noe, Table of n, a(n) for n=1..200

Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Eric Weisstein's World of Mathematics, Lucas n-Step Number

Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,1).

FORMULA

G.f.: x(1+2*x+3*x^2+4*x^3)/(1-x-x^2-x^3-x^4).

a(n) = trace of M^n, where M = the 4 X 4 matrix [ 0 1 0 0 / 0 0 1 0 / 0 0 0 1 / 1 1 1 1]. E.g. the trace (sum of diagonal terms) of M^12 = a(12) = 2631 = (108 + 316 + 717 + 1490). - Gary W. Adamson, Feb 22 2004

a(n)=n*sum(k=ceiling(n/5)..n, sum(i=0..(n-k)/4, (-1)^i*binomial(k,k-i)*binomial(n-i*4-1,k-1))/k), n>0. [Vladimir Kruchinin, Jan 20 2012]

MAPLE

A001648:=-(1+2*z+3*z**2+4*z**3)/(-1+z+z**2+z**3+z**4); # Conjectured by Simon Plouffe in his 1992 dissertation.

MATHEMATICA

Rest@ CoefficientList[ Series[(4 - 3 x - 2 x^2 - x^3)/(1 - x - x^2 - x^3 - x^4), {x, 0, 40}], x] (* Or *)

a[0] = 4; a[1] = 1; a[2] = 3; a[3] = 7; a[4] = 15; a[n_] := 2*a[n - 1] - a[n - 5]; Array[a, 33] (* Robert G. Wilson v *)

LinearRecurrence[{1, 1, 1, 1}, {1, 3, 7, 15}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *)

PROG

(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+3*x^2+4*x^3)/(1-x-x^2-x^3-x^4)+x*O(x^n), n))

(Maxima) a(n):=n*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-i*4-1, k-1), i, 0, ((n-k)/4))/k, k, ceiling(n/5), n); /* Vladimir Kruchinin, Jan 20 2012 */

CROSSREFS

Cf. A000288, A073817.

Sequence in context: A078869 A011890 A131076 * A051054 A001649 A213215

Adjacent sequences:  A001645 A001646 A001647 * A001649 A001650 A001651

KEYWORD

nonn,easy,changed

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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 19 05:11 EST 2014. Contains 252175 sequences.