OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
FORMULA
a(n) = 1 + floor( n*(n^2 + 12*n + 47)/60 ).
From G. C. Greubel, Mar 24 2023: (Start)
a(n) = floor( binomial(n+5,3)/10 ).
G.f.: (1 -x +x^3 -x^6 +2*x^7 -2*x^8 +2*x^9 -x^10 +x^11 -x^12 +x^14 +x^15 -2*x^16 +x^17)/((1-x)^3*(1-x^20)). (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 3, -1}, {1, 2, 3, 5, 8, 12, 16, 22, 28, 36, 45, 56, 68, 81, 96, 114, 133, 154, 177, 202, 230, 260, 292}, 53] (* Ray Chandler, Jul 17 2015 *)
Table[Floor[Binomial[n+5, 5]/Binomial[n+2, 2]], {n, 0, 60}] (* or *) Table[ Floor[((3+n)(4+n)(5+n))/60], {n, 0, 60}] (* Harvey P. Dale, Sep 04 2017 *)
Floor[Binomial[Range[5, 65], 3]/10] (* G. C. Greubel, Mar 24 2023 *)
PROG
(Magma) [Floor(Binomial(n+5, 3)/10): n in [0..60]]; // G. C. Greubel, Mar 24 2023
(SageMath) [(binomial(n+5, 3)//10) for n in range(61)] # G. C. Greubel, Mar 24 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 01 2003
STATUS
approved