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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Project Euler, Problem 463: A weird recurrence relation

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.

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

Adjacent sequences:  A239444 A239445 A239446 * A239448 A239449 A239450

KEYWORD

nonn

AUTHOR

Olivier Pirson, Mar 18 2014

EXTENSIONS

More terms from Alois P. Heinz, May 19 2014

STATUS

approved

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Last modified April 21 15:55 EDT 2021. Contains 343156 sequences. (Running on oeis4.)