|
|
A302576
|
|
Numbers k such that k/10 + 1 is a square.
|
|
1
|
|
|
-10, 0, 30, 80, 150, 240, 350, 480, 630, 800, 990, 1200, 1430, 1680, 1950, 2240, 2550, 2880, 3230, 3600, 3990, 4400, 4830, 5280, 5750, 6240, 6750, 7280, 7830, 8400, 8990, 9600, 10230, 10880, 11550, 12240, 12950, 13680, 14430, 15200, 15990, 16800, 17630, 18480, 19350, 20240
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Equivalently, numbers k such that (k + 10)*10 is a square.
The positive terms belong to the fourth column of the array in A185781.
|
|
LINKS
|
|
|
FORMULA
|
O.g.f.: -10*x*(1 - 3*x)/(1 - x)^3.
E.g.f.: -10*x*(1 - x)*exp(x).
a(n) = a(2-n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = 10*n*(n - 2) = 10*A067998(n).
|
|
MATHEMATICA
|
Table[10 n (n - 2), {n, 1, 50}]
|
|
PROG
|
(PARI) vector(50, n, nn; 10*n*(n-2))
(Maxima) makelist(10*n*(n-2), n, 1, 50);
(GAP) List([1..50], n -> 10*n*(n-2));
(Julia) [10*n*(n-2) for n in 1:50] |> println
(Sage) [10*n*(n-2) for n in (1..50)]
(Python) [10*n*(n-2) for n in range(1, 50)]
(Magma) [10*n*(n-2): n in [1..50]];
|
|
CROSSREFS
|
After -10, subsequence of A174133 because a(n) = ((n-1)^2-1)*(3^2+1).
Similar lists of k for which k/j + 1 is a square: A067998 (j=1), A054000 (j=2), A067725 (j=3), A134582 (j=4), A067724 (j=5), A067726 (j=6), A067727 (j=7), second bisection of A067728 (j=8), A147651 (j=9), this sequence (j=10), A067705 (j=11), second bisection of A067707 (j=12).
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|