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A239447
Partial sums of A030101.
1
0, 1, 2, 5, 6, 11, 14, 21, 22, 31, 36, 49, 52, 63, 70, 85, 86, 103, 112, 137, 142, 163, 176, 205, 208, 227, 238, 265, 272, 295, 310, 341, 342, 375, 392, 441, 450, 491, 516, 573, 578, 615, 636, 689, 702, 747, 776, 837, 840, 875, 894, 945, 956, 999, 1026, 1085
OFFSET
0,3
FORMULA
a(4n) = 6 a(2n) - 5 a(n) - 3 a(n-1) - 1.
a(4n + 1) = 2 a(2n+1) + 4 a(2n) - 6 a(n) - 2 a(n-1) - 1.
a(4n + 2) = 3 a(2n+1) + 3 a(2n) - 6 a(n) - 2 a(n-1) - 1.
a(4n + 3) = 6 a(2n+1) - 8 a(n) - 1.
MATHEMATICA
Accumulate[Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2], {n, 0, 80}]] (* Harvey P. Dale, Jan 10 2023 *)
PROG
(Python) A = {0: 0, 1: 1, 2: 2, 3: 5}
.
def a(n):
....a_n = A.get(n)
....if a_n is not None:
........return a_n
.
....q, r = divmod(n, 4)
....if r == 0:
........a_n = a(q*2)*6 - a(q)*5 - a(q - 1)*3 - 1
....elif r == 1:
........a_n = a(q*2 + 1)*2 + a(q*2)*4 - a(q)*6 - a(q - 1)*2 - 1
....elif r == 2:
........a_n = a(q*2 + 1)*3 + a(q*2)*3 - a(q)*6 - a(q - 1)*2 - 1
....else:
........a_n = a(q*2 + 1)*6 - a(q)*8 - 1
.
....A[n] = a_n # memoization
.
....return a_n
CROSSREFS
Cf. A030101.
Sequence in context: A341446 A015613 A135013 * A336527 A293398 A180323
KEYWORD
nonn
AUTHOR
Olivier Pirson, Mar 18 2014
EXTENSIONS
More terms from Alois P. Heinz, May 19 2014
STATUS
approved