A196507 a(n) = n*(3*n^2 + 6*n + 1).

0, 10, 50, 138, 292, 530, 870, 1330, 1928, 2682, 3610, 4730, 6060, 7618, 9422, 11490, 13840, 16490, 19458, 22762, 26420, 30450, 34870, 39698, 44952, 50650, 56810, 63450, 70588, 78242, 86430, 95170, 104480, 114378, 124882

Offset: 0

Author

R. J. Mathar, Oct 03 2011

Keywords

• nonn
• easy

References

• Jolley, Summation of Series, Dover (1961), eq. 45 on page 8.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[n*(3*n^2+6*n+1): n in [0..30]]; // Vincenzo Librandi, Oct 05 2011

Formula

a(n) = 2*5 + 5*8 + 8*11 + ... + (3*k-1)*(3*k+2) + ... (n terms) = n*A100536(n+1).

G.f.: -2*x*(-5 - 5*x + x^2) / (x-1)^4.

E.g.f.: exp (x)*(10*x + 15*x^2 + 3*x^3). - Franck Maminirina Ramaharo, Nov 22 2018