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

0,6

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).

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)

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 *)

Prog

(PARI) a(n)=n*(n-1)*(n-2)*(n-3)\29 \\ Charles R Greathouse IV, Oct 18 2022
(Magma) [Floor(24*Binomial(n, 4)/29): n in [0..60]]; // G. C. Greubel, Oct 27 2024
(SageMath) [24*binomial(n, 4)//29 for n in range(61)] # G. C. Greubel, Oct 27 2024

Crossrefs

Cf. A011915.

Sequence in context: A223764 A102653 A102650 * A203286 A028346 A356728

Adjacent sequences: A011936 A011937 A011938 * A011940 A011941 A011942

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved