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A268368 An eventually quasi-quadratic sequence satisfying a Hofstadter-like recurrence. 5
0, 1, 0, 4, 4, 4, 3, 12, 8, 4, 3, 24, 12, 4, 3, 40, 16, 4, 3, 60, 20, 4, 3, 84, 24, 4, 3, 112, 28, 4, 3, 144, 32, 4, 3, 180, 36, 4, 3, 220, 40, 4, 3, 264, 44, 4, 3, 312, 48, 4, 3, 364, 52, 4, 3, 420, 56, 4, 3, 480, 60, 4, 3, 544, 64, 4, 3, 612, 68, 4, 3, 684 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)), with the initial conditions: a(n) = 0 if n <= 0; a(1) = 0, a(2) = 1, a(3) = 0, a(4) = 4, a(5) = 4, a(6) = 4, a(7) = 3.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

a(2) = 1, a(3) = 0; otherwise a(4n) = 2n^2+2n, a(4n+1) = 4n, a(4n+2) = 4, a(4n+3) = 3.

From Colin Barker, Jun 22 2017: (Start)

G.f.: x^2*(1 + 4*x^2 + 4*x^3 + x^4 + 3*x^5 - 4*x^7 - 5*x^8 - 6*x^9 + 3*x^12 + 3*x^13) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3).

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n>12.

(End)

PROG

(PARI) concat(0, Vec(x^2*(1 + 4*x^2 + 4*x^3 + x^4 + 3*x^5 - 4*x^7 - 5*x^8 - 6*x^9 + 3*x^12 + 3*x^13) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3) + O(x^100))) \\ Colin Barker, Jun 22 2017

CROSSREFS

Cf. A005185, A188670, A244477, A264757, A267501.

Sequence in context: A073259 A174987 A214926 * A274947 A279406 A171408

Adjacent sequences:  A268365 A268366 A268367 * A268369 A268370 A268371

KEYWORD

nonn,easy

AUTHOR

Nathan Fox, Feb 23 2016

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.