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A008260 Coordination sequence for Paracelsian. 1
1, 4, 10, 21, 37, 57, 81, 109, 142, 180, 222, 268, 318, 373, 433, 497, 565, 637, 714, 796, 882, 972, 1066, 1165, 1269, 1377, 1489, 1605, 1726, 1852, 1982, 2116, 2254, 2397, 2545, 2697, 2853, 3013, 3178, 3348, 3522, 3700, 3882, 4069, 4261, 4457, 4657, 4861 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Inorganic Crystal Structure Database: Collection Code 24690.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

R. W. Grosse-Kunstleve, Coordination Sequences and Encyclopedia of Integer Sequences

R. W. Grosse-Kunstleve, G. O. Brunner and N. J. A. Sloane, Algebraic Description of Coordination Sequences and Exact Topological Densities for Zeolites, Acta Cryst., A52 (1996), pp. 879-889.

Sean A. Irvine, Generating Functions for Coordination Sequences of Zeolites, after Grosse-Kunstleve, Brunner, and Sloane

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

FORMULA

From N. J. A. Sloane, Mar 15 1996: (Start)

a(5*k)   = 55*k^2 + 2 with k>0 and a(0)=1,

a(5*k+1) = 55*k^2 + 22*k + 4,

a(5*k+2) = 55*k^2 + 44*k + 10,

a(5*k+3) = 55*k^2 + 66*k + 21,

a(5*k+4) = 55*k^2 + 88*k + 37. (End)

G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 5*x^4 + 3*x^5 + 2*x^6 + x^7)/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)). - Bruno Berselli, Jul 24 2013

a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n>7. - Colin Barker, Feb 15 2018

MATHEMATICA

LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 4, 10, 21, 37, 57, 81, 109}, 50] (* Harvey P. Dale, Jul 29 2015 *)

PROG

(PARI) Vec((1 + x)*(1 + x + 2*x^2 + 3*x^3 + 2*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Feb 15 2018

CROSSREFS

Sequence in context: A047963 A301014 A301009 * A016430 A008034 A008134

Adjacent sequences:  A008257 A008258 A008259 * A008261 A008262 A008263

KEYWORD

nonn,easy

AUTHOR

Ralf W. Grosse-Kunstleve

STATUS

approved

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Last modified April 21 06:10 EDT 2021. Contains 343146 sequences. (Running on oeis4.)