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A186537 G.f.: Sum( x^k/(1-2*x+x^k), k=1..oo). 2
0, 1, 2, 4, 7, 12, 20, 34, 58, 101, 178, 318, 574, 1046, 1920, 3548, 6593, 12312, 23092, 43480, 82154, 155716, 295984, 564050, 1077400, 2062311, 3955186, 7598756, 14622318, 28179338, 54379520, 105071498, 203254164, 393607534, 763001000, 1480458656, 2875091021, 5588152920, 10869906136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This arose while studying the properties of A079500.

LINKS

N. J. A. Sloane and Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 257 terms from N. J. A. Sloane)

FORMULA

G.f.: -(1+x^2+ 1/(x-1) )/(1-x)*( 1 + x*(x-1)^3*(1-x+x^3)/( Q(0)- x*(x-1)^3*(1-x+x^3)) ), where Q(k) = (x+1)*(2*x-1)*(1-x)^2 + x^(k+2)*(x+x^2+x^3-2*x^4-1 - x^(k+3) + x^(k+5)) - x*(-1+2*x-x^(k+3))*(1-2*x+x^2+x^(k+4)-x^(k+5))*(-1+4*x-5*x^2+2*x^3 - x^(k+2)- x^(k+5) + 2*x^(k+3) - x^(2*k+5) + x^(2*k+6))/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 14 2013

MAPLE

add( x^k/(1-2*x+x^k), k=1..61); series(%, x, 60); seriestolist(%);

# second Maple program:

b:= proc(n, m) option remember; `if`(n=0, 1,

      `if`(m=0, add(b(n-j, j), j=1..n),

      add(b(n-j, min(n-j, m)), j=1..min(n, m))))

    end:

a:= proc(n) a(n):= `if`(n=0, 0, b(n-1, 0)+a(n-1)) end:

seq(a(n), n=0..40);  # Alois P. Heinz, May 01 2014

MATHEMATICA

b[n_, m_] := b[n, m] = If[n == 0, 1, If[m == 0, Sum[b[n-j, j], {j, 1, n}], Sum[b[n-j, Min[n-j, m]], {j, 1, Min[n, m]}]]]; a[n_] := If[n == 0, 0, b[n-1, 0] + a[n-1]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 05 2014, after Alois P. Heinz *)

CROSSREFS

First differences give A079500.

Sequence in context: A340217 A289000 A289028 * A079970 A079816 A178937

Adjacent sequences:  A186534 A186535 A186536 * A186538 A186539 A186540

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 23 2011

STATUS

approved

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Last modified September 18 03:09 EDT 2021. Contains 347504 sequences. (Running on oeis4.)