OFFSET
0,6
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).
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].
EXAMPLE
a(9) = 0+0+0+0+1+1+2+3+4+6 = 17.
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]
Accumulate[Floor[Range[0, 60]^2/13]] (* Harvey P. Dale, Jan 11 2026 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Hoang Xuan Thanh, Jun 22 2025
STATUS
approved