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A084684 Degrees of certain maps. 6
1, 2, 4, 8, 13, 20, 28, 38, 49, 62, 76, 92, 109, 128, 148, 170, 193, 218, 244, 272, 301, 332, 364, 398, 433, 470, 508, 548, 589, 632, 676, 722, 769, 818, 868, 920, 973, 1028, 1084, 1142, 1201, 1262, 1324, 1388, 1453, 1520, 1588, 1658, 1729, 1802, 1876, 1952, 2029, 2108, 2188, 2270, 2353, 2438, 2524, 2612, 2701, 2792, 2884, 2978, 3073, 3170, 3268, 3368, 3469, 3572 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of binary strings of length n with no substrings equal to 0001, 1001, or 1011. - R. H. Hardin, Aug 14 2009

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Jarmo Hietarinta and Claude Viallet, Discrete Painlevé I and singularity confinement in projective space, Chaos, Solitons and Fractals 11 (2000), pp. 29-32.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

a(n) = (6*n^2 + 9 - (-1)^n)/8. - Charles R Greathouse IV, Sep 10 2014

G.f.: ( 1+2*x^3 ) / ( (1+x)*(1-x)^3 ). - R. J. Mathar, Sep 11 2014

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). - Colin Barker, Sep 11 2014

a(n) = a(-n) for all n in Z. - Michael Somos, Feb 08 2015

a(n) - a(n-1) = A001651(n), a(n+1) - a(n-1) = 3*n for all n in Z. - Michael Somos, Feb 08 2015

(a(n) - a(n+1))^2 - (2*a(n) + a(n+1)) + 4 = 3*n/2 + 1 for all even n in Z. - Michael Somos, Feb 08 2015

0 = -4 + a(n)*(-a(n+1) + a(n+2)) + a(n+1)*(+3 + a(n+1) - a(n+2)) for all n in Z. - Michael Somos, Feb 08 2015

A122958(n-1) = p(-1) where p(x) is the unique degree-n polynomial such that p(k) = a(k) for k = 0, 1, ..., n for all n>1. - Michael Somos, Feb 08 2015

EXAMPLE

G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 13*x^4 + 20*x^5 + 28*x^6 + 38*x^7 + ...

MATHEMATICA

a[ n_] := Quotient[ 6 n^2 + 10, 8]; (* Michael Somos, Feb 08 2015 *)

LinearRecurrence[{2, 0, -2, 1}, {1, 2, 4, 8}, 70] (* Harvey P. Dale, Jul 21 2021 *)

PROG

(PARI) a(n)=(6*n^2 + 9 - (-1)^n)/8 \\ Charles R Greathouse IV, Sep 10 2014

(PARI) {a(n) = (6*n^2 + 10) \ 8}; /* Michael Somos, Feb 08 2015 */

CROSSREFS

Cf. A064863, A056107 (bisection), A077588 (bisection).

Cf. A001651, A122958.

Sequence in context: A030503 A245094 A164486 * A011907 A056133 A172131

Adjacent sequences:  A084681 A084682 A084683 * A084685 A084686 A084687

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 16 2003

EXTENSIONS

More terms from Charles R Greathouse IV, Sep 10 2014

STATUS

approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)