This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216414 a(n) = (-1)^(n-3)*binomial(n,3) - 1. 1
 0, -5, 9, -21, 34, -57, 83, -121, 164, -221, 285, -365, 454, -561, 679, -817, 968, -1141, 1329, -1541, 1770, -2025, 2299, -2601, 2924, -3277, 3653, -4061, 4494, -4961, 5455, -5985, 6544, -7141, 7769, -8437, 9138, -9881, 10659, -11481, 12340, -13245, 14189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS a(n-1) gives the number of times the sum of all numbers divisible by all combinations of n fixed, distinct primes below a certain limit have to be added in counting the numbers divisible by at least 4 distinct primes below a certain limit. LINKS Andrew Howroyd, Table of n, a(n) for n = 3..1000 Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1). FORMULA a(n) = (-1)^(n+1)*binomial(n,3) + 1. |a(n+1)-a(n) | = A000330(n). G.f. x*(5+6*x+4*x^2+x^3) / ( (x-1)*(1+x)^4 ). - R. J. Mathar, Sep 07 2012 a(n) = sum(k=1..n-3, (-1)^k*C(n+1,k)). - Mircea Merca, Feb 07 2013 EXAMPLE Let k be the number of values below 10^16 that are divisible by at least four distinct primes below 100. Let b(n) be the sum of all values below 10^16 that are divisible by all combinations of n fixed, distinct primes below 100. Then k = b(4) - 5*b(5) + 9*b(6) - 21*b(7) + 34*b(8) - 57*b(9) + 83*b(10) - 121*b(11) + 164*b(12) - 221*b(13). PROG (PARI) for(n=3, n=50, print((-1)^(n-3)*binomial(n, 3)-1)) CROSSREFS Cf. A002663 (number of times an element with n distinct prime factors will be counted, while taking the count for all the combinations of elements with some 4 fixed, distinct prime factors). Sequence in context: A068481 A146827 A297360 * A147018 A081883 A049744 Adjacent sequences:  A216411 A216412 A216413 * A216415 A216416 A216417 KEYWORD sign,easy AUTHOR V. Raman, Sep 07 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)