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

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

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(24*Binomial(n,4)/25): n in [0..80]]; // 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 *)

SageMath

[24*binomial(n,4)//25 for n in range(81)] # G. C. Greubel, Nov 02 2024

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