OFFSET
1,3
COMMENTS
Integer solutions of x + y = (x - y)^6. If x = a(n) then y = a(n - (-1)^n).
LINKS
Winston de Greef, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
FORMULA
G.f.: x^2*(1+30*x-4*x^2+150*x^3+6*x^4+150*x^5-4*x^6+30*x^7+x^8) / ((1-x)^7*(1+x)^6).
a(n) = a(n-1) + 6*a(n-2) - 6*a(n-3) - 15*a(n-4) + 15*a(n-5) + 20*a(n-6) - 20*a(n-7) - 15*a(n-8) + 15*a(n-9) + 6*a(n-10) - 6*a(n-11) - a(n-12) + a(n-13).
MAPLE
map(k -> (k*(k^5-1)/2, k*(k^5+1)/2), [$1..100]);
PROG
(PARI) concat(0, Vec(x^2*(1+30*x-4*x^2+150*x^3+6*x^4+150*x^5-4*x^6+30*x^7+x^8)/((1-x)^7*(1+x)^6) + O(x^100)))
(Python)
def A361263(n): return (k:=n+1>>1)*(k**5+1-((n&1)<<1))>>1 # Chai Wah Wu, Mar 22 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thomas Scheuerle, Mar 06 2023
STATUS
approved