A027621 a(n) = n + (n+1)^2 + (n+2)^3 + (n+3)^4.
90, 288, 700, 1440, 2646, 4480, 7128, 10800, 15730, 22176, 30420, 40768, 53550, 69120, 87856, 110160, 136458, 167200, 202860, 243936, 290950, 344448, 405000, 473200, 549666, 635040, 729988, 835200, 951390, 1079296, 1219680
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[n + (n+1)^2 + (n+2)^3 + (n+3)^4: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011
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Maple
seq( (n+3)^2*(n^2 + 7*n + 10), n=0..40); # G. C. Greubel, Aug 05 2022
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Mathematica
Table[Total[Table[(n+i)^(i+1),{i,0,3}]],{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{90,288,700,1440,2646},40] (* Harvey P. Dale, Jun 08 2017 *) -
Sage
[i+(i+1)^2+(i+2)^3+(i+3)^4 for i in range(0,40)] # Zerinvary Lajos, Jul 03 2008
Formula
G.f.: 16/(1-x) + 16/(1-x)^2 + 16/(1-x)^3 + 18/(1-x)^4 + 24/(1-x)^5. - R. J. Mathar, Feb 22 2008
a(n) = (n+3)^2*(n^2 + 7*n + 10). - Bruno Berselli, Aug 05 2011
E.g.f.: (90 + 198*x + 107*x^2 + 19*x^3 + x^4)*exp(x). - G. C. Greubel, Aug 05 2022