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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
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.
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).
a(n) = A033583(n-1) - 10. - Altug Alkan, Apr 10 2018
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).
Sequence in context: A051906 A171809 A167302 * A214122 A084033 A340955
KEYWORD
sign,easy
AUTHOR
Bruno Berselli, Apr 10 2018
STATUS
approved