A385894 a(n) = n^5/5 + n^3/3 + 7*n/15.

0, 1, 10, 59, 228, 669, 1630, 3479, 6728, 12057, 20338, 32659, 50348, 74997, 108486, 153007, 211088, 285617, 379866, 497515, 642676, 819917, 1034286, 1291335, 1597144, 1958345, 2382146, 2876355, 3449404, 4110373, 4869014, 5735775, 6721824, 7839073, 9100202, 10518683

Offset: 0

Author

Stefano Spezia, Jul 12 2025

Keywords

• nonn
• easy

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 2.5.17 on page 77.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..4000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A058031.

Programs

Magma

[n^5/5 + n^3/3 + 7*n/15: n in [0..35]]; // Vincenzo Librandi, Jul 22 2025

Mathematica

a[n_]:=n^5/5+n^3/3+7n/15; Array[a,36,0]

Formula

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.

G.f.: x*(1 + 4*x + 14*x^2 + 4*x^3 + x^4)/(1 - x)^6.

E.g.f.: exp(x)*x*(15 + 60*x + 80*x^2 + 30*x^3 + 3*x^4)/15.

a(n) - a(n-1) = A058031(n) for n > 0.