A326501
a(n) = Sum_{k=0..n} (-k)^k.
Original entry on oeis.org
1, 0, 4, -23, 233, -2892, 43764, -779779, 15997437, -371423052, 9628576948, -275683093663, 8640417354593, -294234689237660, 10817772136320356, -427076118244539019, 18019667955465012597, -809220593930871751580, 38537187481365665823844
Offset: 0
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a:= proc(n) option remember; `if`(n<0, 0, (-n)^n+a(n-1)) end:
seq(a(n), n=0..23); # Alois P. Heinz, Sep 12 2019
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RecurrenceTable[{a[0] == 1, a[n] == a[n-1] + (-n)^n}, a, {n, 0, 23}] (* Jean-François Alcover, Nov 27 2020 *)
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{a(n) = sum(k=0, n, (-k)^k)}
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from itertools import accumulate, count, islice
def A326501_gen(): # generator of terms
yield from accumulate((-k)**k for k in count(0))
A326501_list = list(islice(A326501_gen(),10)) # Chai Wah Wu, Jun 18 2022
A343931
Numbers k such that Sum_{j=1..k} (-j)^j == 0 (mod k).
Original entry on oeis.org
1, 3, 4, 11, 131, 188, 324, 445, 3548, 8284, 201403, 253731, 564084, 1812500, 4599115
Offset: 1
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q[n_] := Divisible[Sum[PowerMod[-k, k, n], {k, 1, n}], n]; Select[Range[8500], q] (* Amiram Eldar, May 04 2021 *)
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isok(n) = sum(k=1, n, Mod(-k, n)^k)==0;
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from itertools import accumulate, count, islice
def A343931_gen(): # generator of terms
yield 1
for i, j in enumerate(accumulate((-k)**k for k in count(1)),start=2):
if j % i == 0:
yield i
A343931_list = list(islice(A343931_gen(),10)) # Chai Wah Wu, Jun 18 2022
A271427
a(n) = 7^n - a(n-1) for n>0, a(0)=0.
Original entry on oeis.org
0, 7, 42, 301, 2100, 14707, 102942, 720601, 5044200, 35309407, 247165842, 1730160901, 12111126300, 84777884107, 593445188742, 4154116321201, 29078814248400, 203551699738807, 1424861898171642, 9974033287201501, 69818233010410500, 488727631072873507, 3421093417510114542
Offset: 0
a(2) = 7^2 - a(2-1) = 49 - 7 = 42.
a(4) = 7^4 - a(4-1) = 2401 - 301 = 2100.
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LinearRecurrence[{6, 7}, {0, 7}, 30]
Table[7 (7^n - (-1)^n)/8, {n, 0, 30}]
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vector(50, n, n--; 7*(7^n-(-1)^n)/8) \\ Altug Alkan, Apr 13 2016
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for n in range(0,10**2):print((int)((7*(7**n-(-1)**n))/8))
# Soumil Mandal, Apr 14 2016
Showing 1-3 of 3 results.
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