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A028310
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Expansion of (1 - x + x^2) /(1 - x)^2 in powers of x.
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22
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1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Molien series for ring of Hamming weight enumerators of self-dual codes (with respect to Euclidean inner product) of length n over GF(4).
Engel expansion of e (see A006784 for definition) [when offset by 1]. - Henry Bottomley, Dec 18 2000
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LINKS
| M. Somos, Rational Function Multiplicative Coefficients
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).
Index to sequences with linear recurrences with constant coefficients, signature (2,-1).
Index entries for Molien series
Index entries for sequences related to Engel expansions
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FORMULA
| Binomial transform is A005183. - Paul Barry, Jul 21 2003
G.f.: (1 - x + x^2) / (1 - x)^2 = (1 - x^6) /((1 - x) * (1 - x^2) * (1 - x^3)) = (1 + x^3) / ((1 - x) * (1 - x^2)). a(0) = 1, a(n) = n if n>0.
Euler transform of length 6 sequence [ 1, 1, 1, 0, 0, -1]. - Michael Somos Jul 30 2006
a(n) = Sum_{k, 0<=k<=n} A123110(n,k). [From Philippe DELEHAM, Oct 06 2009]
a(n) = a(a(n-1)+a(n-a(n-3)) [From Roger L. Bagula, Feb 13 2010]
E.g.f: 1+x*exp(x). [From Wolfdieter Lang, May 03 2010]
a(n)=sqrt(floor[A204503(n+3)/9]). - M. F. Hasler, Jan 16 2012
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EXAMPLE
| 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8 + 9*x^9 + ...
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MAPLE
| a:= n-> `if` (n=0, 1, n):
seq (a(n), n=0..60);
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MATHEMATICA
| Contribution from Roger L. Bagula, Feb 13 2010: (Start)
f[0] = 0; f[1] = 1; f[2] = 1; f[3] = 1;
f[n_] := f[n] = f[f[n - 1]] + f[n - f[n - 3]];
Table[f[n], {n, 0, 50}] (End)
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PROG
| (PARI) {a(n) = (n==0) + max(n, 0)} /* Michael Somos Feb 02 2004 */
(PARI) A028310(n)=n+!n \\ - M. F. Hasler, Jan 16 2012
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CROSSREFS
| Apart from the extra initial 1, same as A000027.
Cf. A004001, A005229. [From Roger L. Bagula, Feb 13 2010]
Sequence in context: A069782 A088480 A061019 * A097045 A118759 A118760
Adjacent sequences: A028307 A028308 A028309 * A028311 A028312 A028313
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KEYWORD
| nonn,easy,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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