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Accumulate[Table[FromDigits[Reverse[IntegerDigits[n, 2]], 2], {n, 0, 80}]] (* Harvey P. Dale, Jan 10 2023 *)

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Project Euler, <a href="httphttps://projecteuler.net/problem=463">Problem 463: A weird recurrence relation</a>

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Project Euler, <a href="http://projecteuler.net/problem=463">Problem 463</a>

Project Euler, <a href="http://projecteuler.net/problem=463">Problem 463</a>

Alois P. Heinz, <a href="/A239447/b239447.txt">Table of n, a(n) for n = 0..10000</a>

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

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.

nonn,more

nonn

More terms from Alois P. Heinz, May 19 2014

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Partial sumsums of A030101.

Partial sum of A030101

Cf. A030101.

nonn,more,changed

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N. J. A. Sloane: "Partial sums" is correct.