A277384 Least common multiple of n + 4 and n - 4.

15, 6, 7, 0, 9, 10, 33, 12, 65, 42, 105, 16, 153, 90, 209, 60, 273, 154, 345, 48, 425, 234, 513, 140, 609, 330, 713, 96, 825, 442, 945, 252, 1073, 570, 1209, 160, 1353, 714, 1505, 396, 1665, 874, 1833, 240, 2009, 1050, 2193, 572, 2385, 1242, 2585, 336, 2793

Offset

1,1

Comments

The recurrence for the general case lcm(n+k, n-k) is b(n) = 3*b(n-2*k) - 3*b(n-4*k) + b(n-6*k) for n>6*k.

Links

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

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

Formula

a(n) = 3*a(n-8)-3*a(n-16)+a(n-24) for n>27.

G.f.: x*(15 +6*x +7*x^2 +9*x^4 +10*x^5 +33*x^6 +12*x^7 +20*x^8 +24*x^9 +84*x^10 +16*x^11 +126*x^12 +60*x^13 +110*x^14 +24*x^15 +123*x^16 +46*x^17 +51*x^18 -7*x^20 -6*x^21 -15*x^22 -4*x^23 -30*x^24 -12*x^25 -14*x^26) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3).

Maple

A277384:=n->lcm(n+4, n-4): seq(A277384(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2017

Mathematica

Table[LCM[n + 4, n - 4], {n, 1, 25}] (* G. C. Greubel, Oct 12 2016 *)

Prog

(PARI) a(n) = lcm(n+4, n-4)
(PARI) Vec(x*(15 +6*x +7*x^2 +9*x^4 +10*x^5 +33*x^6 +12*x^7 +20*x^8 +24*x^9 +84*x^10 +16*x^11 +126*x^12 +60*x^13 +110*x^14 +24*x^15 +123*x^16 +46*x^17 +51*x^18 -7*x^20 -6*x^21 -15*x^22 -4*x^23 -30*x^24 -12*x^25 -14*x^26) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3) + O(x^60))

Crossrefs

Cf. A066830 (k=1), A249859 (k=2), A249860 (k=3).

Cf. A277385.

Sequence in context: A064107 A116907 A351199 * A040214 A364351 A111298

Adjacent sequences: A277381 A277382 A277383 * A277385 A277386 A277387

Keyword

nonn,easy

Author

Colin Barker, Oct 12 2016

Status

approved