A011939 a(n) = floor( n*(n-1)*(n-2)*(n-3)/29 ).

0, 0, 0, 0, 0, 4, 12, 28, 57, 104, 173, 273, 409, 591, 828, 1129, 1506, 1969, 2532, 3207, 4009, 4953, 6053, 7328, 8793, 10468, 12372, 14524, 16944, 19656, 22680, 26040, 29760, 33864, 38380, 43332, 48748, 54657, 61088, 68069, 75633, 83809, 92631, 102132, 112345, 123306, 135049, 147612, 161031, 175345

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1).

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(24*Binomial(n,4)/29): n in [0..60]]; // G. C. Greubel, Oct 27 2024

Mathematica

Table[Floor[Times@@(n-Range[0,3])/29],{n,0,60}] (* or *) LinearRecurrence[{4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1},{0,0,0,0,0,4,12,28,57,104,173,273,409,591,828,1129,1506,1969,2532,3207,4009,4953,6053,7328,8793,10468,12372,14524,16944,19656,22680,26040,29760},60] (* Harvey P. Dale, Jun 09 2024 *)
Floor[24*Binomial[Range[0,60], 4]/29] (* G. C. Greubel, Oct 27 2024 *)

PARI

a(n)=n*(n-1)*(n-2)*(n-3)\29 \\ Charles R Greathouse IV, Oct 18 2022

SageMath

[24*binomial(n,4)//29 for n in range(61)] # G. C. Greubel, Oct 27 2024

Formula

From Chai Wah Wu, Aug 02 2020: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-29) - 4*a(n-30) + 6*a(n-31) - 4*a(n-32) + a(n-33) for n > 32.

G.f.: x^5*(4 -4*x +4*x^2 +x^3 -x^5 +5*x^6 -4*x^7 +5*x^8 -x^9 +3*x^11 -2*x^12 +4*x^13 -2*x^14 +3*x^15 -x^17 +5*x^18 -4*x^19 +5*x^20 -x^21 +x^23 +4*x^24 -4*x^25 +4*x^26)/((1-x)^4*(1-x^29)). (End)

Extensions

More terms added by G. C. Greubel, Oct 27 2024