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A094200 a(n)=16*n^4+32*n^3+36*n^2+20*n+3. 2
3, 107, 699, 2547, 6803, 15003, 29067, 51299, 84387, 131403, 195803, 281427, 392499, 533627, 709803, 926403, 1189187, 1504299, 1878267, 2318003, 2830803, 3424347, 4106699, 4886307, 5772003, 6773003, 7898907, 9159699, 10565747 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let x(n)=(1/2)*(-(2*n+1)+sqrt((2*n+1)^2+4)) and f(k)=(-1)*sum(i=1,k,sum(j=1,i,(-1)^floor(j*x(n)))), then a(n)=k is the least integer k>0 such that f(k)=0.

REFERENCES

B. Cloitre, On parity properties of certain Beatty sequences, in preparation 2004

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

a(0)=3, a(1)=107, a(2)=699, a(3)=2547, a(4)=6803, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Jul 23 2013

MATHEMATICA

Table[16n^4+32n^3+36n^2+20n+3, {n, 0, 30}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {3, 107, 699, 2547, 6803}, 30] (* Harvey P. Dale, Jul 23 2013 *)

PROG

(PARI) a(n)=16*n^4+32*n^3+36*n^2+20*n+3

CROSSREFS

Cf. A094201, A085005.

Sequence in context: A301369 A142509 A023325 * A003705 A146214 A261997

Adjacent sequences:  A094197 A094198 A094199 * A094201 A094202 A094203

KEYWORD

nonn

AUTHOR

Benoit Cloitre, May 25 2004

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)