1,2

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

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

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

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

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

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 (qntmpkt(AT)yahoo.com), Feb 22 2004

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

(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))

Cf. A000288, A073817.

Sequence in context: A078869 A011890 A131076 this_sequence A051054 A001649 A001276

Adjacent sequences: A001645 A001646 A001647 this_sequence A001649 A001650 A001651

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).