A295620 - OEIS

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A295620

Solution of the complementary equation a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4) + b(n-4), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, and (a(n)) and (b(n)) are increasing complementary sequences.

1, 2, 3, 4, 12, 20, 49, 85, 177, 304, 578, 979, 1765, 2953, 5150, 8538, 14570, 23997, 40352, 66149, 110094, 179867, 297172, 484313, 795934, 1294823, 2119684, 3443689, 5621258, 9123343, 14860404, 24100573, 39192618, 63526879, 103182816, 167177109, 271286602

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OFFSET

0,2

COMMENTS

The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values.

LINKS

Table of n, a(n) for n=0..36.

Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.

EXAMPLE

a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4, b(0) = 5, b(1) = 6, b(2) = 7, b(3) = 8, so that

b(4) = 9 (least "new number")

a(4) = a(3) + 3*a(2) -2*a(1) - 2*a(0) + b(0) = 12