A380463 Partial sums of floor(n^2/13).
0, 0, 0, 0, 1, 2, 4, 7, 11, 17, 24, 33, 44, 57, 72, 89, 108, 130, 154, 181, 211, 244, 281, 321, 365, 413, 465, 521, 581, 645, 714, 787, 865, 948, 1036, 1130, 1229, 1334, 1445, 1562, 1685, 1814, 1949, 2091, 2239, 2394, 2556, 2725, 2902, 3086, 3278, 3478
Offset: 0
Examples
a(9) = 0+0+0+0+1+1+2+3+4+6 = 17.
Links
- Hoang Xuan Thanh, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
Programs
-
Mathematica
LinearRecurrence[{3, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 3,-1}, {0, 0, 0, 0, 1, 2, 4, 7, 11, 17, 24, 33, 44, 57, 72, 89}, 60] -
PARI
a(n)=(2*n^3+3*n^2-35*n+48)\78 - ((n+6)%13<6)
-
SageMath
(((x^4+x^9)*(1-x+x^2))/((1-x)^3*(1-x^13))).series(x, 52).coefficients(x, sparse=False) # Stefano Spezia, Jun 23 2025
Formula
G.f.: ((x^4+x^9)*(1-x+x^2))/((1-x)^3*(1-x^13)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-13) - 3*a(n-14) + 3*a(n-15) - a(n-16).
a(n) = floor((2*n^3 + 3*n^2 - 35*n + 48)/78) - [(n+6 mod 13)<6].