A011935 a(n) = floor( n*(n-1)*(n-2)*(n-3)/25 ).

0, 0, 0, 0, 0, 4, 14, 33, 67, 120, 201, 316, 475, 686, 960, 1310, 1747, 2284, 2937, 3720, 4651, 5745, 7022, 8500, 10200, 12144, 14352, 16848, 19656, 22800, 26308, 30206, 34521, 39283, 44520, 50265, 56548, 63403, 70862, 78960, 87734, 97219, 107452, 118473

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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1).

Formula

a(n) = +4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +a(n-25) -4*a(n-26) +6*a(n-27) -4*a(n-28) +a(n-29). - R. J. Mathar, Apr 15 2010

G.f.: x^5*(4 -2*x +x^2 +3*x^3 -2*x^4 +5*x^5 -3*x^6 +4*x^7 -2*x^8 +3*x^9 +2*x^10 -2*x^11 +2*x^12 +3*x^13 -2*x^14 +4*x^15 -3*x^16 +5*x^17 -2*x^18 +3*x^19 +x^20 -2*x^21 +4*x^22)/((1-x)^4*(1-x^25)). - G. C. Greubel, Nov 02 2024

Mathematica

Floor[24*Binomial[Range[0, 80], 4]/25] (* G. C. Greubel, Nov 02 2024 *)
Table[Floor[Times@@(n-Range[0, 3])/25], {n, 0, 40}]  (* 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, 1, -4, 6, -4, 1}, {0, 0, 0, 0, 0, 4, 14, 33, 67, 120, 201, 316, 475, 686, 960, 1310, 1747, 2284, 2937, 3720, 4651, 5745, 7022, 8500, 10200, 12144, 14352, 16848, 19656}, 40] (* Harvey P. Dale, Jan 18 2025 *)

Prog

(Magma) [Floor(24*Binomial(n, 4)/25): n in [0..80]]; // G. C. Greubel, Nov 02 2024
(SageMath) [24*binomial(n, 4)//25 for n in range(81)] # G. C. Greubel, Nov 02 2024

Crossrefs

Cf. A011915.

Sequence in context: A124786 A322009 A228272 * A266020 A351930 A185441

Adjacent sequences: A011932 A011933 A011934 * A011936 A011937 A011938

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved