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A000969 G.f.: (1+x+2*x^2)/((1-x)^2*(1-x^3)).
(Formerly M2630 N1042)
25
1, 3, 7, 12, 18, 26, 35, 45, 57, 70, 84, 100, 117, 135, 155, 176, 198, 222, 247, 273, 301, 330, 360, 392, 425, 459, 495, 532, 570, 610, 651, 693, 737, 782, 828, 876, 925, 975, 1027, 1080, 1134, 1190, 1247, 1305, 1365, 1426, 1488, 1552, 1617, 1683, 1751, 1820, 1890 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.

P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.

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.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

FORMULA

a(n) = floor( (2*n+3)*(n+1)/3 ). Or, a(n) = (2*n+3)*(n+1)/3 but subtract 1/3 if n == 1 mod 3. - N. J. A. Sloane, May 05 2010.

a(2^k-2) = A139250(2^k-1), k >= 1. - Omar E. Pol, Feb 13 2010

a(n) = Sum_{i=0..n} floor(4*i/3). - Enrique Pérez Herrero, Apr 21 2012

a(n) = +2*a(n-1) -1*a(n-2) +1*a(n-3) -2*a(n-4) +1*a(n-5). - Joerg Arndt, Apr 22 2012

a(n) = A014105(n+1) = A258708(n+3,n). - Reinhard Zumkeller, Jun 23 2015

MAPLE

A000969:=-(1+z+2*z**2)/(z**2+z+1)/(z-1)**3; # Simon Plouffe in his 1992 dissertation

MATHEMATICA

f[x_, y_] := Floor[ Abs[ y/x - x/y]]; Table[ f[3, 2 n^2 + n + 2], {n, 53}] (* Robert G. Wilson v, Aug 11 2010 *)

PROG

(Haskell)

a000969 = flip div 3 . a014105 . (+ 1)  -- Reinhard Zumkeller, Jun 23 2015

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -2, 1, -1, 2]^n*[1; 3; 7; 12; 18])[1, 1] \\ Charles R Greathouse IV, May 10 2016

CROSSREFS

Cf. A004773 (first differences), A092498 (partial sums).

Cf. A139250, A160165, A258708, A014105.

Sequence in context: A257941 A257944 A005228 * A194117 A122250 A169679

Adjacent sequences:  A000966 A000967 A000968 * A000970 A000971 A000972

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 27 14:52 EDT 2017. Contains 288790 sequences.