OFFSET
1,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
FORMULA
G.f.: x^2*(1+3*x+16*x^2+12*x^3+23*x^4+5*x^5+4*x^6)/((1-x)^6*(1+x)^5).
a(n) = (2*n-1+(-1)^n)*(2*n+3+(-1)^n)*(16*n^3-n^2+10*n-4-(n^2+6*n+4)*(-1)^n)/3840.
a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) - 10*a(n-4) + 10*a(n-5) + 10*a(n-6) - 10*a(n-7) - 5*a(n-8) + 5*a(n-9) + a(n-10) - a(n-11).
EXAMPLE
a(6) = 1^2*5^2 + 2^2*4^2 + 3^2*3^2 = 25 + 64 + 81 = 170.
MATHEMATICA
CoefficientList[Series[x (1 + 3 x + 16 x^2 + 12 x^3 + 23 x^4 + 5 x^5 + 4 x^6)/((1 - x)^6 (1 + x)^5), {x, 0, 80}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 28 2021
STATUS
approved