cp's OEIS Frontend

A361263 Numbers of the form k*(k^5 +- 1)/2.

%I A361263 #25 Mar 22 2023 22:00:47
%S A361263 0,1,31,33,363,366,2046,2050,7810,7815,23325,23331,58821,58828,131068,
%T A361263 131076,265716,265725,499995,500005,885775,885786,1492986,1492998,
%U A361263 2413398,2413411,3764761,3764775,5695305,5695320,8388600,8388616,12068776,12068793,17006103,17006121,23522931,23522950
%N A361263 Numbers of the form k*(k^5 +- 1)/2.
%C A361263 Integer solutions of x + y = (x - y)^6. If x = a(n) then y = a(n - (-1)^n).
%H A361263 Winston de Greef, <a href="/A361263/b361263.txt">Table of n, a(n) for n = 1..10000</a>
%H A361263 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
%F A361263 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).
%F A361263 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).
%p A361263 map(k -> (k*(k^5-1)/2, k*(k^5+1)/2), [$1..100]);
%o A361263 (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)))
%o A361263 (Python)
%o A361263 def A361263(n): return (k:=n+1>>1)*(k**5+1-((n&1)<<1))>>1 # _Chai Wah Wu_, Mar 22 2023
%Y A361263 Cf. A006003, A021003, A027441, A057587, A057590, A135503, A168029.
%Y A361263 Cf. A167963 (bisection).
%K A361263 nonn,easy
%O A361263 1,3
%A A361263 _Thomas Scheuerle_, Mar 06 2023